EXPLANATION:
Given;
We are given a cubic function as shown in the attached image.
Required;
We are required to determine the average rate of change of the function on the interval,
[tex]-7\leq x\leq-3[/tex]
Step-by-step solution;
To solve this question using the line segment from the point where the value of the input is -7 up to -3, we would have the following;
Observe that the change in y is from 0 to -8 that is -8, while the change in x is from -7 to -3, that is 4.
In other words, what we have is;
[tex]\begin{gathered} \Delta y=-8 \\ \Delta x=4 \end{gathered}[/tex]
The average rate of change is given by the formula;
[tex]ROC=\frac{\Delta y}{\Delta x}[/tex][tex]ROC=\frac{-8}{4}[/tex][tex]Rate\text{ }of\text{ }change=-2[/tex]
ANSWER:
The average rate of change on the given interval therefore is -2.
