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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Tuesday, May 02, 2006

Answers to Mini-Exam #6

(1) D
(2) D
(3) A
(4) B
(5) A

free response question

(a) Because g is the derivative of the function ƒ, ƒ will attain a relative minimum at ta point where g=0 and where g is negative to the left of that point and positive to the right of it. This occurs at x=6.

(b) Bcause g is the derivative of the function ƒ, ƒ will attain a relative amximum at a point where g=0 and where g is positive to the left of that point and negative to the right of it. This occurs at x=3.

(c) We are trying to find the area between the graph and the x-axis from x=-3 to x=6. From x=-3 to x=3, the region is a semicircle of radius 3, so the area is 9π/2.
From x=3 to x=6, the region is a semicircle of radius 3/2, so the area is 9π/8.
We substract the latter region from the former to obtain: (9π/2) - (9π/8) = (27π/8)

(d) Because ƒ''(x) = g'(x), we are looking for points where the derivative of g is zero. This occurs at the horizontal tangent lines at x=0, x=4.5, and x=7.5.



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