Math for Econ I, Homework Assignment 5 Instructor: Antonio De Rosa Due: Thursday, October 19th, during Lecture New York University Instructions: IMPORTANT: PLEASE WRITE THE NUMBER OF YOUR RECITATION SECTION (NOT ONLY THE CLASS SECTION NUMBER 006)! IT WILL BE IMPORTANT TO GIVE YOU BACK THE HOMEWORKS DURING THE RECITATION YOU ATTEND! Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work you will not be given any credit. Write your name and recitation section number. Staple your homework if you have multiple pages! 1. (3 pts) Suppose f (x) = ax2 + bx + c, where a, b, c are constants. For what value (or values) of x is f 0 (x) = 0? 2. (6 pts) If f (3) = 1, f 0 (3) = 3, g(3) = 5, and g 0 (3) = 4, find: (a) (3 pts) (f g)0 (3). Note: this is the derivative of (f times g), not the derivative of the composition (f g). \u0010 f \u00110 (b) (3 pts) (3). g 3. (4 pts) The derivative g 0 of some function g is graphed below. On what intervals is g increasing? For what x-value(s) is the tangent line for g horizontal? 4. (4 pts) Let f (x) = |x|. Graph f 0 (x). (note: f 0 (0) will be undefined! Drawing the picture of f should help you graph the derivative: |x| is a piecewise function consisting of two lines.) 5. (3 pts) Differentiate f (x) = 3 8x + 3 x1/4