The graph of the function f(x) is given below. 2. 1 a. Draw the anti-derivative F(x) of f(x) such that F(0) = 0. b. Draw the anti-derivative G(x) of f(x) such that G(0) = 1. c. Find F(2), F(5) and G(5). d. For what values of x, the function F(x) is concave up? y = f(x) 9 (9,-1) 10 ·X

The graph of fx=1/x is a .

and g(x) = 2x¹ + 5x - 1. 3. Let f(x) = x¹/3 and g(x) A. Write out the equations for all four functions: ƒ(x), ƒ'(x), g(x), and g'(x). B. In each of the following, combine the functions f, f', g, and g' as given to write and simplify a function of x. 1. f(g(x)) II. f' (g(x)).g'(x) III. g(f(x)) IV._g(f(x))• f'(x)

For the function y = f(x) given graphically below, find all x numbers such that f(x) = 2 Ox = -3, 3 x does not exist with this property Ox = -3, -1, 1, 3 Ox =-2, 2 X = -2,