Question

use the graph of ( f(x) ) to discuss the graph of ( y = f(x) ). organize your conclusions in a table and sketch a possible graph of ( y = f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function ( f ) is decreasing on the subinterval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. the function ( f ) is never decreasing.

Explanation:

Step1: Recall the relationship between \(y = f(x)\) and \(y=f^{\prime}(x)\)

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

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

Looking at the graph of \(y=f^{\prime}(x)\), we find the intervals where \(y = f^{\prime}(x)<0\). From the graph, we can observe that \(f^{\prime}(x)<0\) on the interval \((- 16,16)\)

Answer:

A. The function \(f\) is decreasing on the sub - interval(s) \((-16,16)\)