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:

(a)

Step1: Identify local maximum

A local maximum occurs at a point where the function changes from increasing to decreasing.
From the graph, at \(x = 0\), the function has a local maximum.

Step2: Find the value of local maxima

The \(y -\)value at \(x = 0\) is \(y=3\).

(b)

Step1: Identify local minimum

A local minimum occurs at a point where the function changes from decreasing to increasing.
From the graph, at \(x=- 2\) and \(x = 1\), the function has local minima.

Answer:

(a)

• The value(s) of \(x\) at which \(f\) has a local maximum is \(x = 0\).
• The local maxima is \(y = 3\).

(b)

• The value(s) of \(x\) at which \(f\) has a local minimum is/are \(x=-2,1\).