Math 125 - Calculus I - Take-home Quiz 2 Name: Fall 2017 1. Due date: September 11, 2017 (Monday) 2. Answer ALL questions. 3. You may not use notes or other references. 4. Approved calculators are permitted. However, you should write down systematically the steps in the workings. 5. Answers with no explanation will not receive full credit. Question 1. [4 points] Sketch a possible graph of y = f (x) given the following three conditions about the derivative: f 0 (x) = 0 for x 2, x = 0, and x 2; f 0 (x) > 0 for 2 < x < 0; f 0 (x) < 0 for 0 < x < 2. 1 Question 2. Consider the function g defined by [6 points] g(x) = 1 . x (i) Use the definition to find the derivative of g(x) at x = 1. (3 points) (ii) Use the above answer to find the equation of the tangent line to the graph y = g(x) at x = 1. points) END OF THE QUIZ 2 (3