Chapter 2.1, Problem 57E

7. Clearly explain why the Vertical Line Test works relation is a function. (Do not explain how it works, in identifying explain if the graph of a why it works).

Looking at the graph of f(x), determine the following below. Show your work. Assume ends of the graph continue. 10- |(0, 8) (0.189, 8.096) -5 G (-2, 0) (1.702, 0) 10 (-3.,523, –4.689) a. Location(s) where f "(x) < 0 b. Location(s) where f'(x) has a minimum c. Sign (positive/negative/zero) of f"(x) at Point G d. Sign (positive/negative/zero) of f '(x) at Point F

Choose the correct answer Please number of choose only please to all . 1-For what values of x is the function f(x)=-x2-2x+15  decreasing? A)(-infinity,-2].  B)(-infinity,-1)  C)[-2,infinity)  D)(-1, infinity) 2-For what values of x is the function f(x)=1/2x(x2-3x-9) decreasing? A)(-3,1) B) (-1, 3)      C)[-1, 3]  D)(-infinity,-1)union(3, infinity) 3-For what values of x is the function f(x)=4x2+4x-3  increasing? A)(-infinity,-1/2) B)(-infinity,-1/2]. C)(-1/2, infinity). D)[-1/2, infinity) 4-For what values of x is the function  F(x)=4x3+12x2-3  concave down ? A)(-infinity,-1) B)(-infinity,-2). C)(-1, infinity). D)(-2, infinity) 5-For what values of x is the function f(x)=4x3+12x2-3  concave up? A)(-infinity,-1) B)(-infinity,-2). C)(-1, infinity). D)(-2, infinity) 6- The critical values of f(x) = x+ 1/x is A) {0}  B) {1,-3}   C){1,-1}   D){2,-2})