1. Find all critical numbers of the function. 2. Find any critical numbers of the function.
|
|
- Damian Smith
- 6 years ago
- Views:
Transcription
1 1. Find all critical numbers of the function. a. critical numbers: *b. critical numbers: c. critical numbers: d. critical numbers: e. no critical numbers 2. Find any critical numbers of the function. a. 0 b. c. d. *e. 3. Locate the absolute extrema of the function on the closed interval.
2 a. absolute maximum: absolute minimum: b. absolute maximum: absolute minimum: *c. absolute maximum: absolute minimum: d. absolute maximum: absolute minimum: e. absolute maximum: absolute minimum: 4. Determine whether Rolle's Theorem can be applied to the function on the closed interval [ 1,3]. If Rolle's Theorem can be applied, find all values of c in the open interval ( 1,3) such that *a. Rolle's Theorem applies; c = 1 b. Rolle's Theorem applies; c = 2 c. Rolle's Theorem applies; c = 0 d. Rolle's Theorem applies; c = 1 e. Rolle's Theorem does not apply
3 5. Determine whether the Mean Value Theorem can be applied to the function on the closed interval [3,9]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (3,9) such that. *a. MVT applies; c = 6 b. MVT applies; c = 7 c. MVT applies; c = 4 d. MVT applies; c = 5 e. MVT applies; c = 8 6. A plane begins its takeoff at 2:00 P.M. on a 2200-mile flight. After 12.5 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 100 miles per hour. a. By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 303 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 303 mi/hr and decelerating from 303 mi/hr. b. By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 152 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 152 mi/hr and decelerating from 152 mi/hr. *c. By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 88 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 88 mi/hr and decelerating from 88 mi/hr. d. By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 117 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 117 mi/hr and decelerating from 117 mi/hr. e. By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 176 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 176 mi/hr and decelerating from 176 mi/hr. 7. Find a function f that has derivative and with graph passing through the point (5,6).
4
5 a. b. c. *d. e. 8. Identify the open intervals where the function is increasing or decreasing. a. decreasing on b. increasing on c. d. decreasing on ; increasing on *e. 9. Identify the open intervals where the function is increasing or decreasing.
6 a. decreasing: ; increasing: b. decreasing on c. increasing: ; decreasing: *d. increasing: ; decreasing: e. increasing: ; decreasing: 10. For the function : (a) Find the critical numbers of f (if any); (b) Find the open intervals where the function is increasing or decreasing; and (c) Apply the First Derivative Test to identify all relative extrema. Then use a graphing utility to confirm your results.
7 a. (a) x = 0, (b) increasing: ; decreasing: (c) relative max: ; relative min: b. (a) x = 0, (b) decreasing: ; increasing: (c) relative min: ; relative max: c. (a) x = 0, (b) increasing: ; decreasing: (c) relative max: ; no relative min. *d. (a) x = 0, (b) increasing: ; decreasing: (c) relative max: ; relative min: e. (a) x = 0, (b) decreasing: ; increasing: (c) relative min: ; relative max: 11. The graph of f is shown in the figure. Sketch a graph of the derivative of f.
8 a. b.
9 c. *d. e. The derivative of f does not exist. 12. Determine the open intervals on which the graph of is concave downward or concave upward.
10 a. concave downward on b. concave upward on ; concave downward on *c. concave upward on ; concave downward on d. concave downward on ; concave upward on e. concave downward on ; concave upward on 13. Determine the open intervals on which the graph of is concave downward or concave upward.
11 a. concave downward on ; concave upward on b. concave downward on ; concave upward on c. concave upward on ; concave downward on d. concave downward on ; concave upward on *e. concave upward on ; concave downward on 14. Find the points of inflection and discuss the concavity of the function. a. inflection point at ; concave upward on ; concave downward on b. inflection point at ; concare downward on ;
12 concave upward on c. inflection point at ; concave downward on ; concave upward on d. inflection point at ; concave downward on ; concave upward on *e. inflection point at ; concave upward on ; concave downward on 15. Find the point of inflection of the graph of the function on the interval.
13 a. b. c. *d. e. 16. Find all relative extrema of the function. Use the Second Derivative Test where applicable. a. relative max: ; no relative min b. no relative max; no relative min c. relative min: ; relative max: *d. relative min: ; no relative max e. relative min: ; relative max: 17. Match the function with one of the following graphs.
14 a. b. *c.
15 d. e. 18. Find the limit. a. b. 3 c. d. 3 *e. 5
16 19. Find the limit. a. b. 1 *c. 0 d. e. 20. Find the limit. *a. b. c. 1 d. 7 e. 21. Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.
17 a. b. *c.
18 d. e. 22. A model for the average typing speeds S (words per minute) of a typing student after t weeks of lessons is given by Find. a. 96 words per minute b. 12 words per minute c. 56 words per minute d. 162 words per minute *e. 81 words per minute
19 23. Analyze and sketch a graph of the function. a. b. *c.
20 d. e. 24. Determine the slant asymptote of the graph of. a.
21 b. c. *d. e. no slant asymptotes 25. Analyze and sketch a graph of the function.
22 *a. b. c.
23 d. e. 26. Use the following graph of to sketch a graph of f.
24 a. b. c.
25 *d. e. 27. The graph of f is shown below. For which value of x is zero? a. b. *c. d. e.
26 28. The graph of f is shown below. For which value of x is minimum? a. b. c. *d. e. 29. Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum. a. *b. 28 and 14 c. d. e. 30. Find the point on the graph of the function that is
27 closest to the point. Round all numerical values in your answer to four decimal places.
28 *a. b. c. d. e. 31. Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 529 square meters. a. Dimensions: b. Dimensions: c. Dimensions: *d. Dimensions: e. Dimensions:
ch 3 applications of differentiation notebook.notebook January 17, 2018 Extrema on an Interval
Extrema on an Interval Extrema, or extreme values, are the minimum and maximum of a function. They are also called absolute minimum and absolute maximum (or global max and global min). Extrema that occur
More informationMath2413-TestReview2-Fall2016
Class: Date: Math413-TestReview-Fall016 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of the derivative (if it exists) of the function
More informationCalculus 437 Semester 1 Review Chapters 1, 2, and 3 January 2016
Name: Class: Date: Calculus 437 Semester 1 Review Chapters 1, 2, and 3 January 2016 Short Answer 1. Decide whether the following problem can be solved using precalculus, or whether calculus is required.
More informationTest 3 Review. fx ( ) ( x 2) 4/5 at the indicated extremum. y x 2 3x 2. Name: Class: Date: Short Answer
Name: Class: Date: ID: A Test 3 Review Short Answer 1. Find the value of the derivative (if it exists) of fx ( ) ( x 2) 4/5 at the indicated extremum. 7. A rectangle is bounded by the x- and y-axes and
More informationApplications of Derivatives
Applications of Derivatives Extrema on an Interval Objective: Understand the definition of extrema of a function on an interval. Understand the definition of relative extrema of a function on an open interval.
More informationÏ ( ) Ì ÓÔ. Math 2413 FRsu11. Short Answer. 1. Complete the table and use the result to estimate the limit. lim x 3. x 2 16x+ 39
Math 43 FRsu Short Answer. Complete the table and use the result to estimate the it. x 3 x 3 x 6x+ 39. Let f x x.9.99.999 3.00 3.0 3. f(x) Ï ( ) Ô = x + 5, x Ì ÓÔ., x = Determine the following it. (Hint:
More informationCHAPTER 4: APPLICATIONS OF DERIVATIVES
(Exercises for Section 4.1: Extrema) E.4.1 CHAPTER 4: APPLICATIONS OF DERIVATIVES SECTION 4.1: EXTREMA 1) For each part below, find the absolute maximum and minimum values of f on the given interval. Also
More informationUnit 3 Applications of Differentiation Lesson 4: The First Derivative Lesson 5: Concavity and The Second Derivative
Warmup 1) The lengths of the sides of a square are decreasing at a constant rate of 4 ft./min. In terms of the perimeter, P, what is the rate of change of the area of the square in square feet per minute?
More informationMath 1314 Lesson 12 Curve Sketching
Math 1314 Lesson 12 Curve Sketching One of our objectives in this part of the course is to be able to graph functions. In this lesson, we ll add to some tools we already have to be able to sketch an accurate
More informationAP Calculus AB Semester 1 Practice Final
Class: Date: AP Calculus AB Semester 1 Practice Final Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the limit (if it exists). lim x x + 4 x a. 6
More informationMA 137 Calculus 1 with Life Science Applications Monotonicity and Concavity (Section 5.2) Extrema, Inflection Points, and Graphing (Section 5.
MA 137 Calculus 1 with Life Science Applications Monotonicity and Concavity (Section 52) Extrema, Inflection Points, and Graphing (Section 53) Alberto Corso albertocorso@ukyedu Department of Mathematics
More information1. Determine the limit (if it exists). + lim A) B) C) D) E) Determine the limit (if it exists).
Please do not write on. Calc AB Semester 1 Exam Review 1. Determine the limit (if it exists). 1 1 + lim x 3 6 x 3 x + 3 A).1 B).8 C).157778 D).7778 E).137778. Determine the limit (if it exists). 1 1cos
More informationf (x) = 2x x = 2x2 + 4x 6 x 0 = 2x 2 + 4x 6 = 2(x + 3)(x 1) x = 3 or x = 1.
F16 MATH 15 Test November, 016 NAME: SOLUTIONS CRN: Use only methods from class. You must show work to receive credit. When using a theorem given in class, cite the theorem. Reminder: Calculators are not
More informationMath 265 Test 3 Review
Name: Class: Date: ID: A Math 265 Test 3 Review. Find the critical number(s), if any, of the function f (x) = e x 2 x. 2. Find the absolute maximum and absolute minimum values, if any, of the function
More informationApril 9, 2009 Name The problems count as marked. The total number of points available is 160. Throughout this test, show your work.
April 9, 009 Name The problems count as marked The total number of points available is 160 Throughout this test, show your work 1 (15 points) Consider the cubic curve f(x) = x 3 + 3x 36x + 17 (a) Build
More informationWork the following on notebook paper. You may use your calculator to find
CALCULUS WORKSHEET ON 3.1 Work the following on notebook paper. You may use your calculator to find f values. 1. For each of the labeled points, state whether the function whose graph is shown has an absolute
More informationRolle s Theorem and the Mean Value Theorem. By Tuesday J. Johnson
Rolle s Theorem and the Mean Value Theorem By Tuesday J. Johnson 1 Suggested Review Topics Algebra skills reviews suggested: None Trigonometric skills reviews suggested: None 2 Applications of Differentiation
More informationFinal Examination 201-NYA-05 May 18, 2018
. ( points) Evaluate each of the following limits. 3x x + (a) lim x x 3 8 x + sin(5x) (b) lim x sin(x) (c) lim x π/3 + sec x ( (d) x x + 5x ) (e) lim x 5 x lim x 5 + x 6. (3 points) What value of c makes
More information1. Which one of the following points is a singular point of. f(x) = (x 1) 2/3? f(x) = 3x 3 4x 2 5x + 6? (C)
Math 1120 Calculus Test 3 November 4, 1 Name In the first 10 problems, each part counts 5 points (total 50 points) and the final three problems count 20 points each Multiple choice section Circle the correct
More informationNOTES 5: APPLICATIONS OF DIFFERENTIATION
NOTES 5: APPLICATIONS OF DIFFERENTIATION Name: Date: Period: Mrs. Nguyen s Initial: LESSON 5.1 EXTREMA ON AN INTERVAL Definition of Etrema Let f be defined on an interval I containing c. 1. f () c is the
More informationAP Calculus AB. Chapter IV Lesson B. Curve Sketching
AP Calculus AB Chapter IV Lesson B Curve Sketching local maxima Absolute maximum F I A B E G C J Absolute H K minimum D local minima Summary of trip along curve critical points occur where the derivative
More informationLearning Target: I can sketch the graphs of rational functions without a calculator. a. Determine the equation(s) of the asymptotes.
Learning Target: I can sketch the graphs of rational functions without a calculator Consider the graph of y= f(x), where f(x) = 3x 3 (x+2) 2 a. Determine the equation(s) of the asymptotes. b. Find the
More informationAnalysis of Functions
Lecture for Week 11 (Secs. 5.1 3) Analysis of Functions (We used to call this topic curve sketching, before students could sketch curves by typing formulas into their calculators. It is still important
More informationThe coordinates of the vertex of the corresponding parabola are p, q. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
Mathematics 10 Page 1 of 8 Quadratic Relations in Vertex Form The expression y ax p q defines a quadratic relation in form. The coordinates of the of the corresponding parabola are p, q. If a > 0, the
More informationCollege Calculus Final Review
College Calculus Final Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the following limit. (Hint: Use the graph to calculate the limit.)
More informationMath Honors Calculus I Final Examination, Fall Semester, 2013
Math 2 - Honors Calculus I Final Eamination, Fall Semester, 2 Time Allowed: 2.5 Hours Total Marks:. (2 Marks) Find the following: ( (a) 2 ) sin 2. (b) + (ln 2)/(+ln ). (c) The 2-th Taylor polynomial centered
More informationWhat makes f '(x) undefined? (set the denominator = 0)
Chapter 3A Review 1. Find all critical numbers for the function ** Critical numbers find the first derivative and then find what makes f '(x) = 0 or undefined Q: What is the domain of this function (especially
More informationA.P. Calculus Holiday Packet
A.P. Calculus Holiday Packet Since this is a take-home, I cannot stop you from using calculators but you would be wise to use them sparingly. When you are asked questions about graphs of functions, do
More informationMath Essentials of Calculus by James Stewart Prepared by Jason Gaddis
Math 231 - Essentials of Calculus by James Stewart Prepared by Jason Gaddis Chapter 3 - Applications of Differentiation 3.1 - Maximum and Minimum Values Note We continue our study of functions using derivatives.
More informationSection 3.1 Extreme Values
Math 132 Extreme Values Section 3.1 Section 3.1 Extreme Values Example 1: Given the following is the graph of f(x) Where is the maximum (x-value)? What is the maximum (y-value)? Where is the minimum (x-value)?
More informationSection 4.3 Concavity and Curve Sketching 1.5 Lectures. Dr. Abdulla Eid. College of Science. MATHS 101: Calculus I
Section 4.3 Concavity and Curve Sketching 1.5 Lectures College of Science MATHS 101: Calculus I (University of Bahrain) Concavity 1 / 29 Concavity Increasing Function has three cases (University of Bahrain)
More informationMath Exam 03 Review
Math 10350 Exam 03 Review 1. The statement: f(x) is increasing on a < x < b. is the same as: 1a. f (x) is on a < x < b. 2. The statement: f (x) is negative on a < x < b. is the same as: 2a. f(x) is on
More informationMath Exam 3 Review
Math 142 Spring 2009 c Heather Ramsey Page 1 Math 142 - Exam 3 Review NOTE: Exam 3 covers sections 5.4-5.6, 6.1, 6.2, 6.4, 6.5, 7.1, and 7.2. This review is intended to highlight the material covered on
More informationSection Derivatives and Rates of Change
Section. - Derivatives and Rates of Change Recall : The average rate of change can be viewed as the slope of the secant line between two points on a curve. In Section.1, we numerically estimated the slope
More informationMath 206 Practice Test 3
Class: Date: Math 06 Practice Test. The function f (x) = x x + 6 satisfies the hypotheses of the Mean Value Theorem on the interval [ 9, 5]. Find all values of c that satisfy the conclusion of the theorem.
More informationMATH 2053 Calculus I Review for the Final Exam
MATH 05 Calculus I Review for the Final Exam (x+ x) 9 x 9 1. Find the limit: lim x 0. x. Find the limit: lim x + x x (x ).. Find lim x (x 5) = L, find such that f(x) L < 0.01 whenever 0 < x
More informationMATH 151, Fall 2015, Week 12, Section
MATH 151, Fall 2015, Week 12, Section 5.1-5.3 Chapter 5 Application of Differentiation We develop applications of differentiation to study behaviors of functions and graphs Part I of Section 5.1-5.3, Qualitative/intuitive
More informationAbsolute and Local Extrema. Critical Points In the proof of Rolle s Theorem, we actually demonstrated the following
Absolute and Local Extrema Definition 1 (Absolute Maximum). A function f has an absolute maximum at c S if f(x) f(c) x S. We call f(c) the absolute maximum of f on S. Definition 2 (Local Maximum). A function
More information4.1 Analysis of functions I: Increase, decrease and concavity
4.1 Analysis of functions I: Increase, decrease and concavity Definition Let f be defined on an interval and let x 1 and x 2 denote points in that interval. a) f is said to be increasing on the interval
More information4/16/2015 Assignment Previewer
Practice Exam # 3 (3.10 4.7) (5680271) Due: Thu Apr 23 2015 11:59 PM PDT Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1. Question Details SCalcET7 3.11.023. [1644808] Use the definitions
More information4.3 How Derivatives Aect the Shape of a Graph
11/3/2010 What does f say about f? Increasing/Decreasing Test Fact Increasing/Decreasing Test Fact If f '(x) > 0 on an interval, then f interval. is increasing on that Increasing/Decreasing Test Fact If
More informationWEEK 8. CURVE SKETCHING. 1. Concavity
WEEK 8. CURVE SKETCHING. Concavity Definition. (Concavity). The graph of a function y = f(x) is () concave up on an interval I if for any two points a, b I, the straight line connecting two points (a,
More informationUnit V Applications of Derivatives
Unit V Applications of Derivatives Curve Sketching Inequalities (Not covered in 3205) Polynomial Rational Functions Related Rate Problems Optimization (Max/Min) Problems 1 Inequalities Linear Polynomial
More informationUnit V Applications of Derivatives
Unit V Applications of Derivatives Curve Sketching Inequalities (Covered in 2200) Polynomial Rational Functions Related Rate Problems Optimization (Max/Min) Problems 1 Inequalities Linear Polynomial Rational
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1325 Ch.12 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the location and value of each relative extremum for the function. 1)
More informationMATH section 4.4 Concavity and Curve Sketching Page 1. is increasing on I. is decreasing on I. = or. x c
MATH 0100 section 4.4 Concavity and Curve Sketching Page 1 Definition: The graph of a differentiable function y = (a) concave up on an open interval I if df f( x) (b) concave down on an open interval I
More informationH-Pre-Calculus Targets Chapter I can write quadratic functions in standard form and use the results to sketch graphs of the function.
H-Pre-Calculus Targets Chapter Section. Sketch and analyze graphs of quadratic functions.. I can write quadratic functions in standard form and use the results to sketch graphs of the function. Identify
More information2004 Free Responses Solutions. Form B
Free Responses Solutions Form B All questions are available from www.collegeboard.com James Rahn www.jamesrahn.com Form B AB Area d 8 B. ( ) π ( ) Volume π d π.7 or.8 or ( ) Volume π 9 y 7. or 68 π Form
More informationChapter 3: The Derivative in Graphing and Applications
Chapter 3: The Derivative in Graphing and Applications Summary: The main purpose of this chapter is to use the derivative as a tool to assist in the graphing of functions and for solving optimization problems.
More informationAP Calculus AB Class Starter October 30, Given find. 2. Find for. 3. Evaluate at the point (1,2) for
October 30, 2017 1. Given find 2. Find for 3. Evaluate at the point (1,2) for 4. Find all points on the circle x 2 + y 2 = 169 where the slope is 5/12. Oct 31 6:58 AM 1 October 31, 2017 Find the critical
More informationMcGILL UNIVERSITY FACULTY OF SCIENCE FINAL EXAMINATION MATHEMATICS A CALCULUS I EXAMINER: Professor K. K. Tam DATE: December 11, 1998 ASSOCIATE
NOTE TO PRINTER (These instructions are for the printer. They should not be duplicated.) This examination should be printed on 8 1 2 14 paper, and stapled with 3 side staples, so that it opens like a long
More informationMEMORIAL UNIVERSITY OF NEWFOUNDLAND
MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS FINAL EXAMINATION Solutions Mathematics 1000 FALL 2010 Marks [12] 1. Evaluate the following limits, showing your work. Assign
More informationAP Calculus Worksheet: Chapter 2 Review Part I
AP Calculus Worksheet: Chapter 2 Review Part I 1. Given y = f(x), what is the average rate of change of f on the interval [a, b]? What is the graphical interpretation of your answer? 2. The derivative
More informationdollars for a week of sales t weeks after January 1. What is the total revenue (to the nearest hundred dollars) earned from t = 10 to t = 16?
MATH 7 RIOHONDO SPRING 7 TEST (TAKE HOME) DUE 5//7 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ) A department store has revenue from the sale
More informationExample 1a ~ Like # 1-39
Example 1a ~ Like # 1-39 f(x) = A. The domain is {x x 2 1 0} = {x x 1} DOM: (, 1) ( 1, 1) (1, ) B. The x- and y-intercepts are both 0. C. Since f( x) = f(x), the function f is even. The curve is symmetric
More informationQUIZ ON CHAPTER 4 APPLICATIONS OF DERIVATIVES; MATH 150 FALL 2016 KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS
Math 150 Name: QUIZ ON CHAPTER 4 APPLICATIONS OF DERIVATIVES; MATH 150 FALL 2016 KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% Show all work, simplify as appropriate, and use good form and procedure
More informationPurdue University Study Guide for MA Credit Exam
Purdue University Study Guide for MA 16010 Credit Exam Students who pass the credit exam will gain credit in MA16010. The credit exam is a two-hour long exam with multiple choice questions. No books or
More informationAPPM 1350 Exam 2 Fall 2016
APPM 1350 Exam 2 Fall 2016 1. (28 pts, 7 pts each) The following four problems are not related. Be sure to simplify your answers. (a) Let f(x) tan 2 (πx). Find f (1/) (5 pts) f (x) 2π tan(πx) sec 2 (πx)
More information4.1 & 4.2 Student Notes Using the First and Second Derivatives. for all x in D, where D is the domain of f. The number f()
4.1 & 4. Student Notes Using the First and Second Derivatives Definition A function f has an absolute maximum (or global maximum) at c if f ( c) f ( x) for all x in D, where D is the domain of f. The number
More informationSection 5-1 First Derivatives and Graphs
Name Date Class Section 5-1 First Derivatives and Graphs Goal: To use the first derivative to analyze graphs Theorem 1: Increasing and Decreasing Functions For the interval (a,b), if f '( x ) > 0, then
More informationf'(x) = x 4 (2)(x - 6)(1) + (x - 6) 2 (4x 3 ) f'(x) = (x - 2) -1/3 = x 2 ; domain of f: (-, ) f'(x) = (x2 + 1)4x! 2x 2 (2x) 4x f'(x) =
85. f() = 4 ( - 6) 2 f'() = 4 (2)( - 6)(1) + ( - 6) 2 (4 3 ) = 2 3 ( - 6)[ + 2( - 6)] = 2 3 ( - 6)(3-12) = 6 3 ( - 4)( - 6) Thus, the critical values are = 0, = 4, and = 6. Now we construct the sign chart
More informationMA Lesson 25 Notes Section 5.3 (2 nd half of textbook)
MA 000 Lesson 5 Notes Section 5. ( nd half of tetbook) Higher Derivatives: In this lesson, we will find a derivative of a derivative. A second derivative is a derivative of the first derivative. A third
More information+ 2 on the interval [-1,3]
Section.1 Etrema on an Interval 1. Understand the definition of etrema of a function on an interval.. Understand the definition of relative etrema of a function on an open interval.. Find etrema on a closed
More informationMath 1314 ONLINE Lesson 12
Math 1314 ONLINE Lesson 12 This lesson will cover analyzing polynomial functions using GeoGebra. Suppose your company embarked on a new marketing campaign and was able to track sales based on it. The graph
More informationMathematics 1a, Section 4.3 Solutions
Mathematics 1a, Section 4.3 Solutions Alexander Ellis November 30, 2004 1. f(8) f(0) 8 0 = 6 4 8 = 1 4 The values of c which satisfy f (c) = 1/4 seem to be about c = 0.8, 3.2, 4.4, and 6.1. 2. a. g is
More informationMath 142 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 6.6 and 6.7)
Math 142 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 6.6 and 6.7) Note: This review is intended to highlight the topics covered on the Final Exam (with emphasis on
More informationCHAPTER 3 APPLICATIONS OF THE DERIVATIVE
CHAPTER 3 APPLICATIONS OF THE DERIVATIVE 3.1 Maxima and Minima Extreme Values 1. Does f(x) have a maximum or minimum value on S? 2. If it does have a maximum or a minimum, where are they attained? 3. If
More informationlim 2 x lim lim sin 3 (9) l)
MAC FINAL EXAM REVIEW. Find each of the following its if it eists, a) ( 5). (7) b). c). ( 5 ) d). () (/) e) (/) f) (-) sin g) () h) 5 5 5. DNE i) (/) j) (-/) 7 8 k) m) ( ) (9) l) n) sin sin( ) 7 o) DNE
More informationMATH 151 Engineering Mathematics I
MATH 151 Engineering Mathematics I Spring 2019, WEEK 10 JoungDong Kim Week 10 Section 4.2, 4.3, 4.4 Mean Value Theorem, How Derivatives Affect the Shape of a Graph, Indeterminate Forms and L Hospital s
More informationMTH4100 Calculus I. Week 8 (Thomas Calculus Sections 4.1 to 4.4) Rainer Klages. School of Mathematical Sciences Queen Mary, University of London
MTH4100 Calculus I Week 8 (Thomas Calculus Sections 4.1 to 4.4) Rainer Klages School of Mathematical Sciences Queen Mary, University of London Autumn 2008 R. Klages (QMUL) MTH4100 Calculus 1 Week 8 1 /
More informationCalculus 1st Semester Final Review
Calculus st Semester Final Review Use the graph to find lim f ( ) (if it eists) 0 9 Determine the value of c so that f() is continuous on the entire real line if f ( ), c /, > 0 Find the limit: lim 6+
More informationMath 1314 Lesson 13: Analyzing Other Types of Functions
Math 1314 Lesson 13: Analyzing Other Types of Functions If the function you need to analyze is something other than a polynomial function, you will have some other types of information to find and some
More information2.1 How Do We Measure Speed? Student Notes HH6ed. Time (sec) Position (m)
2.1 How Do We Measure Speed? Student Notes HH6ed Part I: Using a table of values for a position function The table below represents the position of an object as a function of time. Use the table to answer
More information3. Go over old quizzes (there are blank copies on my website try timing yourself!)
final exam review General Information The time and location of the final exam are as follows: Date: Tuesday, June 12th Time: 10:15am-12:15pm Location: Straub 254 The exam will be cumulative; that is, it
More informationMA 113 Calculus I Fall 2009 Exam 3 November 17, 2009
MA 113 Calculus I Fall 2009 Exam 3 November 17, 2009 Answer all of the questions 1-7 and two of the questions 8-10. Please indicate which problem is not to be graded by crossing through its number in the
More informationMathematics Lecture. 6 Chapter. 4 APPLICATIONS OF DERIVATIVES. By Dr. Mohammed Ramidh
Mathematics Lecture. 6 Chapter. 4 APPLICATIONS OF DERIVATIVES By Dr. Mohammed Ramidh OVERVIEW: This chapter studies some of the important applications of derivatives. We learn how derivatives are used
More informationm2413f 4. Suppose that and . Find the following limit b. 10 c. 3 d Determine the limit (if it exists). 2. Find the lmit. a. 1 b. 0 c. d.
m2413f Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find an equation of the line that passes through the point and has the slope. 4. Suppose that and
More informationAB Calc Sect Notes Monday, November 28, 2011
Assignments & Opportunities: I will TRY to have Sketchpad projects back to you next Monday or Tuesday. Tomorrow: p268; 5,22,27,45 & p280; 9 AB Calc Sect 4.3 - Notes Monday, November 28, 2011 Today's Topics
More informationThe plot shows the graph of the function f (x). Determine the quantities.
MATH 211 SAMPLE EXAM 1 SOLUTIONS 6 4 2-2 2 4-2 1. The plot shows the graph of the function f (x). Determine the quantities. lim f (x) (a) x 3 + Solution: Look at the graph. Let x approach 3 from the right.
More information8/6/2010 Assignment Previewer
Week 10 Friday Homework (1328515) Question 12345678910111213141516 1. Question DetailsSCalcET6 4.5.AE.06. [1290372] EXAMPLE 6 Sketch the graph of the function below. (A) The domain is = (-, ). (B) The
More information3.1 ANALYSIS OF FUNCTIONS I INCREASE, DECREASE, AND CONCAVITY
MATH00 (Calculus).1 ANALYSIS OF FUNCTIONS I INCREASE, DECREASE, AND CONCAVITY Name Group No. KEYWORD: increasing, decreasing, constant, concave up, concave down, and inflection point Eample 1. Match the
More informationCURVE SKETCHING. Let's take an arbitrary function like the one whose graph is given below:
I. THE FIRST DERIVATIVE TEST: CURVE SKETCHING Let's take an arbitrary function like the one whose graph is given below: As goes from a to p, the graph rises as moves to the right towards the interval P,
More informationSection 13.3 Concavity and Curve Sketching. Dr. Abdulla Eid. College of Science. MATHS 104: Mathematics for Business II
Section 13.3 Concavity and Curve Sketching College of Science MATHS 104: Mathematics for Business II (University of Bahrain) Concavity 1 / 18 Concavity Increasing Function has three cases (University of
More informationMath 131 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 5.5, 6.1, 6.5, and 6.7)
Math 131 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 5.5, 6.1, 6.5, and 6.7) Note: This collection of questions is intended to be a brief overview of the exam material
More informationM408 C Fall 2011 Dr. Jeffrey Danciger Exam 2 November 3, Section time (circle one): 11:00am 1:00pm 2:00pm
M408 C Fall 2011 Dr. Jeffrey Danciger Exam 2 November 3, 2011 NAME EID Section time (circle one): 11:00am 1:00pm 2:00pm No books, notes, or calculators. Show all your work. Do NOT open this exam booklet
More informationMAT137 Calculus! Lecture 20
official website http://uoft.me/mat137 MAT137 Calculus! Lecture 20 Today: 4.6 Concavity 4.7 Asypmtotes Next: 4.8 Curve Sketching Indeterminate Forms for Limits Which of the following are indeterminate
More informationNovember 13, 2018 MAT186 Week 8 Justin Ko
1 Mean Value Theorem Theorem 1 (Mean Value Theorem). Let f be a continuous on [a, b] and differentiable on (a, b). There eists a c (a, b) such that f f(b) f(a) (c) =. b a Eample 1: The Mean Value Theorem
More informationCalculus 1 Math 151 Week 10 Rob Rahm. Theorem 1.1. Rolle s Theorem. Let f be a function that satisfies the following three hypotheses:
Calculus 1 Math 151 Week 10 Rob Rahm 1 Mean Value Theorem Theorem 1.1. Rolle s Theorem. Let f be a function that satisfies the following three hypotheses: (1) f is continuous on [a, b]. (2) f is differentiable
More information8/6/2010 Assignment Previewer
Week 9 Friday Homework (32849) Question 23456789234567892. Question DetailsSCalcET6 4.2.AE.3. [29377] EXAMPLE 3 To illustrate the Mean Value Theorem with a specific function, let's consider f(x) = 5x 3
More informationTest 3 Review. y f(a) = f (a)(x a) y = f (a)(x a) + f(a) L(x) = f (a)(x a) + f(a)
MATH 2250 Calculus I Eric Perkerson Test 3 Review Sections Covered: 3.11, 4.1 4.6. Topics Covered: Linearization, Extreme Values, The Mean Value Theorem, Consequences of the Mean Value Theorem, Concavity
More informationLesson 10.1 Solving Quadratic Equations
Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One -intercept and all nonnegative y-values b. The verte in the third quadrant and no
More informationSection 1.1: A Preview of Calculus When you finish your homework, you should be able to
Section 1.1: A Preview of Calculus When you finish your homework, you should be able to π Understand what calculus is and how it compares with precalculus π Understand that the tangent line problem is
More informationMAT 1339-S14 Class 4
MAT 9-S4 Class 4 July 4, 204 Contents Curve Sketching. Concavity and the Second Derivative Test.................4 Simple Rational Functions........................ 2.5 Putting It All Together.........................
More informationlim x c) lim 7. Using the guidelines discussed in class (domain, intercepts, symmetry, asymptotes, and sign analysis to
Math 7 REVIEW Part I: Problems Using the precise definition of the it, show that [Find the that works for any arbitrarily chosen positive and show that it works] Determine the that will most likely work
More informationMATH 115 QUIZ4-SAMPLE December 7, 2016
MATH 115 QUIZ4-SAMPLE December 7, 2016 Please review the following problems from your book: Section 4.1: 11 ( true and false) Section 4.1: 49-70 ( Using table or number line.) Section 4.2: 77-83 Section
More informationAP Calculus BC Chapter 4 AP Exam Problems A) 4 B) 2 C) 1 D) 0 E) 2 A) 9 B) 12 C) 14 D) 21 E) 40
Extreme Values in an Interval AP Calculus BC 1. The absolute maximum value of x = f ( x) x x 1 on the closed interval, 4 occurs at A) 4 B) C) 1 D) 0 E). The maximum acceleration attained on the interval
More informationApplications of Differentiation
Applications of Differentiation Definitions. A function f has an absolute maximum (or global maximum) at c if for all x in the domain D of f, f(c) f(x). The number f(c) is called the maximum value of f
More informationMath 125: Exam 3 Review
Math 125: Exam 3 Review Since we re using calculators, to keep the playing field level between all students, I will ask that you refrain from using certain features of your calculator, including graphing.
More information1. Write the definition of continuity; i.e. what does it mean to say f(x) is continuous at x = a?
Review Worksheet Math 251, Winter 15, Gedeon 1. Write the definition of continuity; i.e. what does it mean to say f(x) is continuous at x = a? 2. Is the following function continuous at x = 2? Use limits
More informationMath 1323 Lesson 12 Analyzing functions. This lesson will cover analyzing polynomial functions using GeoGebra.
Math 1323 Lesson 12 Analyzing functions This lesson will cover analyzing polynomial functions using GeoGebra. Suppose your company embarked on a new marketing campaign and was able to track sales based
More information