Question

1. identify the extrema: absolute maximum: x = 2 absolute maximum: x = 0 absolute minimum: x = 1 relative maximum: x = 0 relative maximum: x = 2 relative minimum: x = 1

Explanation:

Step1: Define extrema concepts

Relative extrema occur where the function changes direction. Absolute extrema are the overall highest or lowest points on the domain.

Step2: Analyze the graph

At x = 0 and x = 2, the function changes from increasing to decreasing, so they are relative maxima. At x = 1, the function changes from decreasing to increasing, so it is a relative minimum. There is not enough information to determine absolute extrema from the given graph as we don't know the full domain.

Answer:

Relative maximum: x=0, Relative maximum: x=2, Relative minimum: x=1