Question

1. for the given graph identify the following.

a. what is the relative maximum(s)?
b. where does the relative maximum(s) occur?
c. what is the relative minimum(s)?
d. where does the relative minimum(s) occur?
e. what interval(s) is the graph increasing?
f. what interval(s) is the graph decreasing?

Explanation:

Step1: Identify relative maximum

A relative maximum is a point where the function changes from increasing to decreasing. By observing the graph, we find the peaks.
The relative maximum values are approximately $y = 4$ and $y = 2$.

Step2: Locate x - values for relative maximum

The $x$ - values where the relative maxima occur are the $x$ - coordinates of the peak points. They are $x=-4$ and $x = 2$.

Step3: Identify relative minimum

A relative minimum is a point where the function changes from decreasing to increasing. The relative minimum value is approximately $y=-6$.

Step4: Locate x - values for relative minimum

The $x$ - value where the relative minimum occurs is the $x$ - coordinate of the valley - point, which is $x=-2$.

Step5: Find increasing intervals

The graph is increasing when the $y$ - values are getting larger as $x$ increases. The increasing intervals are $(-6,-4)$ and $(-2,2)$.

Step6: Find decreasing intervals

The graph is decreasing when the $y$ - values are getting smaller as $x$ increases. The decreasing intervals are $(-10,-6)$, $(-4,-2)$ and $(2,10)$.

Answer:

a. $y = 4$ and $y = 2$
b. $x=-4$ and $x = 2$
c. $y=-6$
d. $x=-2$
e. $(-6,-4)$ and $(-2,2)$
f. $(-10,-6)$, $(-4,-2)$ and $(2,10)$