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 \(a\). The value \(f(a)\) is the local - maximum value and \(a\) is the \(x\) - value at which the local maximum occurs.

Step2: Identify local - maximum values from the graph

Looking at the graph, the \(y\) - coordinates (function values) of the local maximum points are \(0\) and \(3\).

Step3: Identify \(x\) - values at which local maxima occur

The \(x\) - coordinates of the local maximum points are \(2\) and \(1.5\) (approximate \(x\) - value for the peak at \(y = 3\)).

Answer:

All local maximum values of \(f\): \(0,3\)
All values at which \(f\) has a local maximum: \(2,1.5\)