Unformatted text preview: approximation in part (c) greater than or less than r ¢(t ) dt in terms of the radius of the balloon. 12 Ú0 r ¢(t ) dt ? Give a reason for your answer. WRITE ALL WORK IN THE PINK EXAM BOOKLET.
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5 2007 AP® CALCULUS AB FREERESPONSE QUESTIONS
6. Let f be the function defined by f ( x ) = k x  ln x for x > 0, where k is a positive constant.
(a) Find f ¢( x ) and f ¢¢( x ) .
(b) For what value of the constant 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.
(c) For a certain value of the constant k, the graph of f has a point of inflection on the xaxis. Find this value
of k. WRITE ALL WORK IN THE PINK EXAM BOOKLET. END OF EXAM © 2007 The College Board. All rights reserved.
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 Spring '09
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 Derivative, Hot air balloon, The College Board

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