Question

the given function (f(x)) is defined on the interval ((-9,9)) and represented by the graph below. find the x - value(s) of all local maxima.

Explanation:

Step1: Recall local maxima definition

A local maximum occurs where the function changes from increasing to decreasing.

Step2: Observe the graph

By looking at the graph of \(y = f(x)\) on the interval \((-9,9)\), we identify the points where the function's behavior changes from increasing to decreasing.

Answer:

The \(x -\)value of the local maximum is the \(x -\)coordinate of the peak point on the graph. From the graph, the \(x -\)value of the local maximum is \(x = 0\).