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Unformatted text preview: maximum velocity, in ft/sec, and at what time
does it occur? Justify your answer.
(d) At what times in the interval 0 t 18 , if any, is the car’s velocity equal to zero? Justify your answer. END OF PART A OF SECTION II Copyright © 2001 by College Entrance Examination Board. All rights reserved.
Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 4 2001 AP® CALCULUS AB FREERESPONSE QUESTIONS
CALCULUS AB
SECTION II, Part B
Time—45 minutes
Number of problems—3
No calculator is allowed for these problems.
4. Let h be a function defined for all x 0 such that h( 4) = 3 and the derivative of h is given by 05 h x = x2  2
for all x 0.
x (a) Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local
maximum, a local minimum, or neither at each of these values. Justify your answers.
(b) On what intervals, if any, is the graph of h concave up? Justify your answer.
(c) Write an equation for the line tangent to the graph of h at x = 4.
(d) Does the line tangent to the graph of h at x = 4 lie above or below the graph of h for x > 4 ? Why? 5. A cubic polynomial function f is...
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 Fall '14

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