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 relative maxima.

Explanation:

Step1: Recall the definition of relative maxima

A relative maximum of a function \(y = f(x)\) is a point \((x,y)\) where the function changes from increasing to decreasing. That is, in a small neighborhood around \(x = a\), \(f(a)\geq f(x)\) for all \(x\) in that neighborhood.

Step2: Analyze the graph

Looking at the graph of the function \(y = f(x)\) on the interval \((-9,9)\). The function has a point where it changes from increasing to decreasing. By observing the graph, we can see that at \(x = 1\), the function reaches a local peak (since to the left of \(x = 1\) the function is increasing and to the right of \(x = 1\) the function is decreasing within a small - enough neighborhood around \(x = 1\)).

Answer:

\(x = 1\)