# trytr - f ( x ) < 0. (c) (4 points) Give all numbers a...

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Exam 1 - Version B 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 ) = (2 - 3 x ) 3 i. (6 points) Compute f 0 ( x ). ii. (6 points) Compute f 00 (1). (b) (8 points) Let K = 5 + q 2 + 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) 4 . 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 - 6 x 6 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 ) =-25 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 inﬂection 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 2000 feet of fence that he wants to use to enclose a rectangular garden. Find the maximum area that Rick’s garden can have....
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## This note was uploaded on 04/04/2010 for the course MATH 113 taught by Professor Staff during the Spring '08 term at Maryland.

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