dsds - f ( x ) < 0. (c) (4 points) Give all...

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Exam 1 - Version A Math 220 Sections 03xx September 28, 2006 Instructions: Put one problem on each answer sheet (use the back if necessary), and put your name, your TA’s name, your section number, and the problem number on each page. Only sign the honor pledge on the first sheet. Show all of your work, and justify your answers. Scientific, but not graphing calculators are allowed. Unless the problem explicitly requests simplification, no simplification is necessary. 1. (a) Let f ( x ) = (3 - 2 x ) 3 . i. (6 points) Compute f 0 ( x ). ii. (6 points) Compute f 00 (1). (b) (8 points) Let K = 3 + q 1 + 2 . Compute dK d . 2. (a) (10 points) Let f ( x ) = x 3 + x 2 - x + 1. Give the equation of the line tangent to the graph of f ( x ) at x = 1. (b) (10 points) Let h ( x ) = ( x 2 - 1) 6 . Compute the average rate of change of h ( x ) over the interval [0 , 1] and the instantaneous rate of change of h ( x ) at x = 0. 3. The graph of a function f defined on the interval - 3 x 3 is shown to the right. (a) (8 points) Give intervals where f 0 ( x ) > 0. (b) (8 points) Give intervals where
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Unformatted text preview: f ( x ) < 0. (c) (4 points) Give all numbers a such that f ( a ) = 0. 4. Let f ( x ) =-9 x-1 x for x > 0 (remember this restricted domain in each part!). (a) (5 points) Locate any critical points ( x and y values) of f ( x ). (b) (5 points) Describe the concavity of f ( x ); that is, list all intervals (if any) where f ( x ) is concave up, list all intervals (if any) where f ( x ) is concave down, and list any inection points (if any). Make sure you clearly label your answers. (c) (5 points) Give any vertical asymptotes of the graph of f ( x ). Bonus (3 points) Give any horizontal or slant asymptotes of the graph of f ( x ). (d) (5 points) Sketch the graph of f ( x ) for x > 0, labeling all critical points and asymptotes. 5. (20 points) Rick has 1200 feet of fence that he wants to use to enclose a rectangular garden. Find the maximum area that Ricks garden can have....
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