Question

determine the extrema of ( f(x) ). then identify the point as a relative maximum or relative minimum.

relative maximum:

relative minimum:

extrema:

Explanation:

Step1: Recall the definition of relative maximum and minimum

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 at points B and D

• At point B: The function changes from decreasing to increasing. So, point B is a relative minimum.
• At point D: The function changes from increasing to decreasing. So, point D is a relative maximum.

Answer:

Relative minimum: B, Relative maximum: D, Extrema: B and D