Unformatted text preview: defined by
f ( x ) = 4 x 3 + ax 2 + bx + k where a, b, and k are constants. The function f has a local minimum at x = 1, and the graph of f has a point
of inflection at x = −2.
(a) Find the values of a and b.
(b) If I 1 0 f ( x ) dx = 32, what is the value of k ? 1 is on the graph of y =
4 6. The function f is differentiable for all real numbers. The point 3, 05 slope at each point x , y on the graph is given by
(a) Find d2y
dx 2 f ( x ), and the dy
= y 2 (6  2 x ).
dx 1 .
4 and evaluate it at the point 3, (b) Find y = f ( x ) by solving the differential equation 0 5 END OF EXAMINATION Copyright © 2001 by College Entrance Examination Board. All rights reserved.
Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 5 05 dy
1
= y 2 6 − 2 x with the initial condition f 3 = .
4
dx...
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 Fall '14
 Derivative, College Entrance Examination Board, college entrance examination, Entrance Examination Board

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