Question

identify the location and value of any relative maxima or minima of the function.

Explanation:

Step1: Understand relative maxima and minima

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

Step2: Analyze the graph

Looking at the graph of \(y = f(x)\):

• At \(x=-2\), the function changes from decreasing to increasing. The \(y\) - value is \(y = - 2\).
• At \(x = 2\), the function changes from increasing to decreasing. The \(y\) - value is \(y=1\).
• At \(x = 4\), the function changes from decreasing to increasing. The \(y\) - value is \(y=-1\) (assuming the grid - based value, since the point is on the \(x = 4\) line and one unit below the \(x\) - axis in the context of the grid).

Answer:

Relative minimum at \((-2,-2)\) and \((4, - 1)\); relative maximum at \((2,1)\)