Name: Math 7 Spring 2021 Quiz 3 Prof. Odom-Chea Quiz 3 (Sections 3.3-3.5): How Derivatives Affect the Shape of a Graph, Asymptotes, Curve Sketching Please show ALL relevant work and indicate reasoning to receive credit. You may use your notes and textbook, but you may NOT consult with the internet! Put your final answers in the appropriate spaces. Do all work on the quiz. This quiz is worth 20 points. √ 1. (10 PTS) Consider the function g(x) = x2 5 − x. (a) Find the first derivative g 0 (x). Be sure to simplify in its factored form if possible. (b) Use the First Derivative Test to find the open intervals on which the function is increasing and decreasing. (c) Identify the function’s local and absolute extreme values, if any, and say where they occur. 1 2. (10 PTS) Consider the function f , whose formula and derivatives are given below: f (x) = 8 , x2 + 4 f 0 (x) = −16x , (x2 + 4)2 f 00 (x) = 16(3x2 − 4) (x2 + 4)3 (a) Find and describe any asymptotes, if any, for f . Use calculus! (b) Find any local extrema, if any for the function f . You may use either the first or second derivative test. (c) Find any inflection points, if any, for the function f . (d) Show a sketch of the function f . 2 Handwritten Academic Honesty Statement After you have completed the quiz, please COPY the following statement on the bottom of this last page and then SIGN and DATE it to attest that you abided by it: I did not receive help on this quiz from anyone other than my instructor. I did not help any other student with this quiz. COPY STATEMENT HERE: Date: Signed Name: 3
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