Give a reason for each answer c for 0 t 7 at what time

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Unformatted text preview: of water in the tank is decreasing. Give a reason for each answer. (c) For 0 £ t £ 7, at what time t is the amount of water in the tank greatest? To the nearest gallon, compute the amount of water at this time. Justify your answer. WRITE ALL WORK IN THE PINK EXAM BOOKLET. © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. -3- 2007 AP® CALCULUS AB FREE-RESPONSE QUESTIONS x f ( x) f ¢( x ) g( x ) g ¢( x ) 1 6 4 2 5 2 9 2 3 1 3 10 –4 4 2 4 –1 3 6 7 3. The functions f and g are differentiable for all real numbers, and g is strictly increasing. The table above gives values of the functions and their first derivatives at selected values of x. The function h is given by h( x ) = f ( g ( x )) - 6. (a) Explain why there must be a value r for 1 < r < 3 such that h(r ) = -5. (b) Explain why there must be a value c for 1 < c < 3 such that h ¢(c ) = -5. (c) Let w...
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This note was uploaded on 12/15/2009 for the course SOCIAL STU 129348437 taught by Professor Phalange during the Spring '09 term at Aberystwyth University.

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