Math 1314 Test 2 Review Lessons 2 8

Transcription

1 Math 1314 Test Review Lessons 8 CASA reservation required. GGB will be provided on the CASA computers. 50 minute exam. 15 multiple choice questions. Do Practice Test for extra practice and extra credit. The following formulas will be provided at CASA for Test. It will be a link. f( x+ h) f( x) f( b) f( a) = h b a C( x) = mx + b = cx + F Rx ( ) = sx or Rx ( ) = xp Px ( ) = Rx ( ) Cx ( ) ht ( ) = 16t + vt 0 + h0 ht ( ) = 4.9t + vt 0 + h Test Review 1

2 1. Given 3 f( x) x x = + and 5x gx ( ) =. Produce the graphs in GGB. x a. Find any local (relative) extrema of f. b. Find any zeros of g. c. Find any points of intersection of functions f and g Test Review

3 . The following table of values gives a company s annual profits in millions of dollars. Rescale the data so that the year 003 corresponds to x = 0. Create a list of points. Year Profits (in millions of dollars) a. Find the linear regression model for the data. b. Find the R value for the cubic regression model. c. Use the linear model to predict the company's profits in The graph of f( x ) is shown below. Which of the following statements is true? a. The b. The c. The does not exist. x exists and it equals 0. x 0 does not exist. x 1314 Test Review 3

4 4. Suppose it exists: x 5, x 1 f x = x < x ( ) 8, 1 3 x + x > x 1 1, determine whether the following 5. 4x x 1 x 5 6. x + 3 x 4 x 8 7. x 5 x 5 x 8. x 0 x x 1314 Test Review 4

5 KNOW THE FOLLOWING Limits at infinity: Compare the degree of the numerator and the degree of the denominator. If the degree of the numerator is smaller than the degree of the denominator, then f ( x) = 0. x g( x) If the degree of the numerator is the same as the degree of the denominator, then f ( x) you can find by making a fraction from the leading coefficients of the x g ( x ) numerator and denominator and then reducing to lowest terms. If the degree of the numerator is larger than the degree of the denominator, then it s best to work the problem viewing the graph in GGB. You can then decide if the function approaches or. This it does not exist, but the or is more descriptive x x x 3 4 x x + 5x 7x 1 x x x x 1 x x 7x 1314 Test Review 5

6 1. The graph of f( x ) is shown below. Which of the following statements is true? I. The function is continuous at x = 3. II. The function is discontinuous at x = 3 because does not exist. III. The function is discontinuous at x = 3 because f(3) does not exist. IV. The function is discontinuous at x = 3 because even though f(3) exists and exists, the two quantities are not equal. x 3 x Using the graph from number 1, state where the function is discontinuous and state the type of discontinuity. x+ 1, x 14. Let f( x) = is the function continuous at x =? If it is discontinuous, 4 x, x > identify the type of discontinuity. We need to check: i. Is f() defined? ii. Check to see if Must check: x exist. x and + x iii. = f()? i.e. Compare #1 and # above. x 1314 Test Review 6

7 15. Find the first and second derivative: f x x x x x 4 3 ( ) = x 16. Let f( x) = x ln( x) e a. Find the slope of the tangent line at x = 3. b. Write the equation of the tangent line at x = Find all x-value(s) on the graph of line is equal to -3. f( x) x 5x 3 = + where the slope of the tangent 1314 Test Review 7

8 18. The distance covered by a car moving along a straight road t seconds after starting from rest is given by f( x) = x + 48x. What is the average velocity of the car over the period of 0 to 3 seconds? 19. The total country-wide box office receipts for a certain long-running movie are 10x approximated by the function f( x) =, where f is measured in millions of dollars x + 4 and x is the number of months since the movie s release. What are the total box office receipts after the second month? 0. A ball is thrown upwards with initial velocity 148 feet per second from the roof of a building that is 78 feet tall. a. When is the velocity zero? b. What is the instantaneous rate of change at 5 seconds? Is the ball falling or rising? c. When will the ball return to the ground? 1314 Test Review 8

9 1. Suppose a manufacturer has monthly fixed costs of $50,000 and production costs of $4 for each item produced. The item sells for $40. Assume all functions are linear. Find the break-even point. Recall: Rx ( ) = Cx ( ). Let y = 5x be a supply equation and y = -6.5x be a demand equation. Find the equilibrium point Test Review 9