A graphing calculator may NOT be used for the following problem.
This graph represents the function f, consisting of a semicircle and three line segments. It can be graphed
using the piecewise function:
(4-6x + 3)2 -5 SX <-1
Ax) = 2 4x + 4
-15x<0
05x<2
10- 3x 25x55
Let g) = 2x + SF(t) dt.
a) Compute g(5). Find g'(5) and evaluate g'(-3).
b) Find the absolute maximum value of g on the closed interval (-5,5). Justify your answer.
c) The second derivative of g is undefined at x = -1, x = 0, and x = 2. Which values are the x-
coordinates of the points of inflection of the graph of g? Justify your answer.