2001 Free Response

# The function f has a local minimum at x 1 and the

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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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