This graph represents the function f, consisting of a semicircle and three line segments. It can be graphed using the piecewise function:
f(x) = {
√4 – (x + 3)^2 –5 ≤ x < –1
4x + 4 –1 ≤ x < 0
4 0 ≤ x < 2
10 – 3x 2 ≤ x ≤ 5
Let g(x) = 2x + ∫ f(t) dt x
.
a) Compute g(5). Find g′(x) 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 xcoordinates of the points of inflection of the graph of g? Justify your answer