Question

the graph of f is given.
(a) on what open intervals is f increasing?
(b) on what open intervals is f decreasing?
(c) what are the x - values of the local extrema?
(d) on what open intervals is f concave up?
(e) on what open intervals is f concave down?
(f) what are the x - values of the inflection points?
(a) on what open intervals is f increasing? select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. the graph of f is increasing on the open interval(s)
(type your answer in interval notation. round to the nearest integer as needed. use a comma to separate answers as needed.)
b. the graph of f is not increasing on any open interval.

Explanation:

Step1: Recall the increasing function condition

A function \(y = f(x)\) is increasing on an interval where \(f^{\prime}(x)>0\).

Step2: Analyze the graph of \(f^{\prime}(x)\)

Looking at the graph of \(f^{\prime}(x)\), we observe that \(f^{\prime}(x)>0\) on the intervals \((-\infty,0)\) and \((16,\infty)\).

Answer:

A. The graph of \(f\) is increasing on the open interval(s) \((-\infty,0),(16,\infty)\)