the graph of f is given. (a) on what open interval: (a) on what open intervals is f increasing? select the…

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.

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.

Answer

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))