AB Practice Exam 1: Free Response

AP Calculus · Axiom Academy

Lesson AB Practice Exam 1: Free Response Practice FRQ problems with guided solutions Free Response Section (6 questions, 90 minutes) Let R be the region bounded by , y = 0 , and x = 4 . (a) Find the area of region R . (b) Find the volume of the solid generated when R is rotated about the x -axis. (c) Region R is the base of a solid whose cross-sections perpendicular to the x -axis are squares. Find the volume. (c) Square cross-sections with side : Let f(x) = x^3 - 6x^2 + 9x + 1 for all x . (a) Find all critical points and classify each. (b) Find the intervals where f is concave up and concave down. (c) Find any inflection points. (d) On what intervals is f both increasing and concave down? (a) f'(x) = 3x^2 - 12x + 9 = 3(x-1)(x-3) . Critical points at x=1 and x=3 . f''(x) = 6x - 12 . f''(1) = -6 0 (local min). (b) . Concave down on , concave up on . (c) Inflection point at (2, f(2)) = (2, 3) . (d) Increasing: . Concave down: . Both: .

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