Question

find the maximum and/or minimum and state whether it is a relative or absolute maximum/minimum. estimate if necessary. (8 points)
3)

Explanation:

Step1: Identify relative maximum

A relative maximum is a point where the function changes from increasing to decreasing. Looking at the graph, there is a peak. Estimating from the grid, the \(y\) - value at the relative maximum is \(y = 2\).

Step2: Identify relative minimum

A relative minimum is a point where the function changes from decreasing to increasing. Estimating from the grid, the \(y\) - value at the relative minimum is \(y=-4\).

Step3: Determine if they are absolute

Since the function extends infinitely upwards (as \(x\to\infty,y\to\infty\)) and infinitely downwards (as \(x\to-\infty,y\to-\infty\)), there are no absolute maximum or minimum.

Answer:

Relative maximum at \(y = 2\), relative minimum at \(y=-4\). There are no absolute maximum or minimum.