Question

f(x)=x^{2}+10
what is the average rate of change of f over the interval -2, -1?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = - 1$, and $f(x)=x^{2}+10$.

Step2: Calculate $f(-2)$

Substitute $x=-2$ into $f(x)$: $f(-2)=(-2)^{2}+10=4 + 10=14$.

Step3: Calculate $f(-1)$

Substitute $x=-1$ into $f(x)$: $f(-1)=(-1)^{2}+10=1 + 10=11$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(-1)-f(-2)}{-1-(-2)}=\frac{11 - 14}{-1 + 2}=\frac{-3}{1}=-3$.

Answer:

$-3$