Math 125 Name: Dr. Young Section #: Fall 2016 Student ID#: Homework Quiz 5 Due: 9/30/2016 Please print and complete the quiz in the space provided below. The quiz is due at the beginning of lecture on the date stated above.

Math 125 Name: Dr. Young Section #: Fall 2016 Student ID#: Homework Quiz 5 Due: 9/30/2016 Please print and complete the quiz in the space provided below. The quiz is due at the beginning of lecture on the date stated above. You must show all work. You may only use your lecture notes and a calculator to complete this quiz. You must complete this quiz independently. Obtaining help from any source other than those listed above will be considered a violation of the Academic Code of Integrity and will be subject to academic disciplinary actions. 1. (10pts) Find the derivatives of the following functions. You may only use the constant rule, constant multiple rule, sum and difference rule, and the power rule. Show all work leading to your answer. (a) (2pts) f(x) = −5x 6 + πx2 − 8 (b) (4pts) f(x) = √3 x 2 − 4 x (c) (4pts) f(x) = x 4 + x − 7 √ x 2. Consider the function f(x) = x 2 − 15 x + 4 . The first and second derivatives of f(x) are given by f 0 (x) = x 2 + 8x + 15 (x + 4)2 and f 00(x) = 2 (x + 4)3 . (a) (5pts) Use a number line to determine the intervals over which f(x) is increasing and decreasing. (b) (5pts) Use a number line to determine the intervals over which f(x) is concave up and concave down. 3. (10pts) Use the limit definition of the derivative at a point to show that f 0 (2) does not exist where f(x) = √3 x − 2.

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