Question

the following is the graph of the function f. estimate the intervals where f is increasing or decreasing. increasing: decreasing: estimate the point at which the graph of f has a local maximum or a local minimum. local maximum: local minimum: question help: video written example submit question

Explanation:

Step1: Define increasing and decreasing

A function is increasing when the graph goes up from left - to - right and decreasing when it goes down from left - to - right.

Step2: Identify increasing intervals

By observing the graph, the function $f$ is increasing on the intervals $(-6,-2)$ and $(3,7)$.

Step3: Identify decreasing intervals

The function $f$ is decreasing on the interval $(-2,3)$.

Step4: Identify local maximum

A local maximum occurs where the function changes from increasing to decreasing. From the graph, the local maximum is at the point $(-2,128)$.

Step5: Identify local minimum

A local minimum occurs where the function changes from decreasing to increasing. From the graph, the local minimum is at the point $(3, - 128)$.

Answer:

Increasing: $(-6,-2),(3,7)$
Decreasing: $(-2,3)$
Local maximum: $(-2,128)$
Local minimum: $(3,-128)$