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? (b) on what open intervals is ( f ) decreasing? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the graph of ( f ) is decreasing 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 decreasing on any open interval.

Explanation:

Step1: Recall the increasing - decreasing rule

A function \(y = f(x)\) is decreasing when \(f^{\prime}(x)<0\).

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

Looking at the graph of \(y = f^{\prime}(x)\), we find the intervals where the graph is below the \(x -\)axis.
From the graph, \(f^{\prime}(x)<0\) on the intervals \((-14,7)\) and \((21,\infty)\) (assuming the \(x -\)intercepts are at \(x=- 14,x = 7,x = 21\) (by approximating to the nearest integers based on the graph's shape)).

Answer:

\((-14,7),(21,\infty)\)