estimate and classify the critical points for the graph of the function.

Explanation:

Step1: Recall critical - point definition

Critical points occur where the derivative is zero or undefined. Visually, they are points where the slope of the tangent line is zero (horizontal tangent) or non - existent.

Step2: Identify horizontal tangents

Looking at the graph, we can estimate the x - values of the points where the tangent line is horizontal. There appears to be a horizontal tangent near (x=- 1).

Step3: Classify the critical point

To classify the critical point, we consider the behavior of the function around it. If the function changes from increasing to decreasing at the critical point, it is a local maximum. If it changes from decreasing to increasing, it is a local minimum. Here, the function is increasing before (x = - 1) and decreasing after (x=-1), so it is a local maximum.

Answer:

There is a critical point at approximately (x=-1), and it is a local maximum.