Question

use the graph to find:
(a) the numbers, if any, at which f has a local maximum. what are these local maxima?
(b) the numbers, if any, at which f has a local minimum. what are these local minima?

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function \(y = f(x)\) occurs at a point \(x = a\) if \(f(a)\geq f(x)\) for all \(x\) in some open interval containing \(a\).

Step2: Analyze the graph

Looking at the graph, at \(x = 0\), the function value \(y=f(0)=3\). For values of \(x\) in an open - interval around \(x = 0\) (say \((-1,1)\)), \(f(0)\) is greater than \(f(x)\) for \(x
eq0\) in that interval.

Answer:

A. The value(s) of \(x\) at which \(f\) has a local maximum is/are \(x = 0\)