AP Calculus AB Class Starter October 30, Given find. 2. Find for. 3. Evaluate at the point (1,2) for

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1 October 30, 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

2 October 31, 2017 Find the critical numbers of the following functions. Determine if the function has an extreme value at the critical number Nov 14 10:55 AM 2

3 November 1, Find the absolute extreme values of the given functions over the indicated interval. (a) (b) 2. If f'(x) > 0 over (0,5), and f(0) = 3 and f(5) = 4, give a possible value of f(2). 3. The concentration C(t) (in mg/cm 3 ) of a drug in a patient's bloodstream after t hours is Find the maximum concentration in the time interval [0,8]. Nov 19 2:08 PM 3

4 November 2, Find the intervals over which the following functions are increasing and the intervals over which the functions are decreasing. Then, find any extrema. (a) (c) (b) 2. The curve has a relative maximum at (2, 1). Find a and b. Nov 14 12:22 PM 4

November 3, 2017 1. Given. Does the Mean Value Theorem apply to the function over the interval [0,2]? If so, find the value of c guaranteed by the theorem. 2. Consider the function f(x) = x sin(x) on the domain [ π/2, π/2].

5 November 3, Given. Does the Mean Value Theorem apply to the function over the interval [0,2]? If so, find the value of c guaranteed by the theorem. 2. Consider the function f(x) = x sin(x) on the domain [ π/2, π/2]. How many values of c in the interval appear to satisfy the Mean Value Theorem? 1. Let f be a function that is differentiable on the open interval (4,8) and continuous on [4,8]. If f(4) = 2, f(6) = 2, and f(8) = 2, which of these must be true? I. f has at least two zeros II. The graph of f has at least one horizontal tangent III. f(5) = 0 (A) None (B) I only (C) I & II (D) I & III (E) ALL Nov 14 12:25 PM 5

November 6, 2017 1. Does Rolle s Theorem apply to on. If so, find the value c guaranteed by the theorem. 2. Explain why the function does not satisfy Rolle s Theorem in the interval [ 1,1].

two hours later. If the legal speed limit is e 4 mph, should Mattie have been ticketed for speeding? Explain your answer. 4. The position of a particle is given by.

6 November 6, Does Rolle s Theorem apply to on. If so, find the value c guaranteed by the theorem. 2. Explain why the function does not satisfy Rolle s Theorem in the interval [ 1,1]. 3. Mattie checked into the tollbooth at mile marker 0 on the Calculus Turnpike, and she checked out at the tollbooth at mile marker 150 exactly two hours later. If the legal speed limit is e 4 mph, should Mattie have been ticketed for speeding? Explain your answer. 4. The position of a particle is given by. Find the minimum velocity of the particle on the interval [0, 4]. Nov 14 12:39 PM 6

November 8, 2017 1. If a is a positive constant, which of the following statements about the function is true.

(B) Function has no extreme values and exactly one inflection point.

(D) Function has two inflection points and two extreme values. 2 Let f be defined by for all x > 0.

7 November 8, If a is a positive constant, which of the following statements about the function is true. (A) Function has at least one extreme value and at least two inflection points. (B) Function has no extreme values and exactly one inflection point. (C) Function has exactly one extreme value and exactly one inflection point. (D) Function has two inflection points and two extreme values. 2 Let f be defined by for all x > 0. And, let k be a positive constant. (a) Find f' and f''. (b) For what value of k does f have a critical point at x = 1? For this value of k, determine whether f has a relative minimum, relative maximum, or neither at x = 1. Justify your answer. 3. Find constants a and b such that the function has a local maximum at. Nov 13 1:44 PM 7

November 9, 2017 1. Which of the following describes the function at the point (1, 1)? A. f is concave up and decreasing B.

Find the interval(s) over which any points of inflection. is concave up. Identify 3. The graph of y = f ' is on the board.

8 November 9, Which of the following describes the function at the point (1, 1)? A. f is concave up and decreasing B. f is concave up and increasing C. f is concave down and decreasing D. f is concave down and increasing 2. Find the interval(s) over which any points of inflection. is concave up. Identify 3. The graph of y = f ' is on the board. Identify the intervals over which the function is increasing, decreasing, concave up, and concave down. Also identify the x coordinate of any relative extrema and inflection points. Justify all answers. Nov 8 6:41 AM 8

and x =3, answer the following questions. 1. Find the x coordinate of all points of inflection on the graph of f. Justify. 2. Find the x coordinate of all extreme values on the graph of f.

9 November 13, 2017 Let f be a continuous function such that f(4) = 6. The graph of f' is on the white board for Given that f is a twice differentiable function and f' has horizontal tangent lines at x = 1 and x =3, answer the following questions. 1. Find the x coordinate of all points of inflection on the graph of f. Justify. 2. Find the x coordinate of all extreme values on the graph of f. Label them as relative maximum or minimum values. Justify. 3. Find the average rate of change of f'(x) on the interval Does the Mean Value Theorem applied on guarantee a value of c on such that f''(x) is equal to this average rate of change? Why or why not? 4. Let g be the function defined by. Find the equation of the tangent line to g at x = 4. Nov 15 2:31 PM 9

Test for Increasing and Decreasing Theorem 5 Let f(x) be continuous on [a, b] and differentiable on (a, b).

Test for Increasing and Decreasing Theorem 5 Let f(x) be continuous on [a, b] and differentiable on (a, b). Definition of Increasing and Decreasing A function f(x) is increasing on an interval if for any two numbers x 1 and x in the interval with x 1 < x, then f(x 1 ) < f(x ). As x gets larger, y = f(x) gets