Question

here is a graph of the function f. use the graph to find the following. if there is more than one answer, separate them with commas. all local maximum values of f: all values at which f has a local maximum:

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function \(y = f(x)\) is a point \((a,f(a))\) such that \(f(a)\geq f(x)\) for all \(x\) in some open interval containing \(a\). Visually, on the graph, it is a “peak” point.

Step2: Identify local maximum values

Looking at the graph, the \(y\) - values of the peak points are \(y = 2\).

Step3: Identify the \(x\) - values of local maximum

The \(x\) - values corresponding to the peak points (where \(y = 2\)) are \(x=-1,2\)

Answer:

All local maximum values of \(f\): \(2\)
All values at which \(f\) has a local maximum: \(-1,2\)