Question

question
identify the local maximum and local minimum of the function shown in the graph below.
provide your answer below:
the local maximum is at ( ) and the local minimum is at ( )

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 the point \((0,1)\), the function changes from decreasing to increasing (local minimum). At the point \((2,4)\), the function changes from increasing to decreasing (local maximum).

Answer:

The local maximum is at \((2,4)\) and the local minimum is at \((0,1)\)