A differentiable function f has a derivative g, where g=f′. A verbal description of the graph of g is given below.
• g(x)<0 for x<−3.
• g(x)=0 at x=−3.
• g(x)>0 for −3<x<1.
• g(x)=0 at x=1.
• g(x)<0 for 1<x<5.
• g decreases on (−∞,−1), increases on (−1,3), and then decreases again on (3,5).
Answer the following, showing clear reasoning in each case.
a. Part 1: (a) Determine the intervals on which f is increasing and the intervals on which f is decreasing.
b. Part 2: (b) Identify each x-coordinate at which f attains a relative maximum or a relative minimum on the open interval (−∞,5). Classify each critical point and justify your classification.
c. Part 3: (c) Determine the intervals on which the graph of f is concave up and the intervals on which it is concave down.
d. Part 4: (d) State all x-coordinates at which the graph of f has a point of inflection and give a brief reason for each.