Question

determine the local maximum and local minimum of the function whose graph is given below
select the correct answer below:
local maximum at $(-2,18)$, local minimum at $(2,-14)$
local maximum at $(-2,-14)$, local minimum at $(2,18)$
local maximum at $(-2,-18)$, local minimum at $(2,14)$
local maximum at $(2,18)$, local minimum at $(-2,-14)$

Explanation:

Step1: Recall the definition of local maximum and minimum

A local maximum is a point where the function changes from increasing to decreasing. A local minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze the graph

Looking at the graph, at \(x = - 2\), the function has a peak (changes from increasing to decreasing). The \(y\) - value at \(x=-2\) is \(18\). At \(x = 2\), the function has a trough (changes from decreasing to increasing). The \(y\) - value at \(x = 2\) is \(-14\).

Answer:

Local maximum at \((-2,18)\), local minimum at \((2,-14)\)