Question

What is the average rate of change of f over the interval -4 < x <5? Give an exact number.

Answer 1

Answer:

$\frac{2}{9}$

Step-by-step explanation:

The average rate of change of a function $f$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

So the average rate of change of our function $f$ here on the interval $[-4,5]$ is $\frac{f(5)-f(-4)}{5-(-4)}=\frac{f(5)-f(-4)}{9}$.

We need to figure out both $f(5)$ and $f(-4)$.

$f(5)$ corresponds to the value in the 2nd column when the first column value is $5$. This number is 4.

$f(5)=4$.

$f(-4)$ corresponds to the value in the 2nd column when the first column value is $-4$. This number is 2.

Let's go back to computing the average rate of change of $f$ on $[-4,5]$:

$\frac{4-2}{9}=\frac{2}{9}$.

The answer is $\frac{2}{9}$.