Question

the graph of f is given. (a) on what open interval: (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 relationship between \(f^{\prime}(x)\) and \(f(x)\)

If \(f^{\prime}(x)>0\) on an open interval \(I\), then the function \(y = f(x)\) is increasing on the interval \(I\).

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

Looking at the graph of \(y=f^{\prime}(x)\), we observe that \(f^{\prime}(x)>0\) when \(x\in(-\infty,-14)\cup(7,21)\) (by estimating the \(x -\) values where the graph of \(y = f^{\prime}(x)\) is above the \(x -\) axis).

Answer:

A. The graph of \(f\) is increasing on the open interval(s) \((-\infty,-14),(7,21)\)