given the function h(x)=x² - 2x - 7, determine the average rate of change of the function over the interval…
given the function h(x)=x² - 2x - 7, determine the average rate of change of the function over the interval -1 ≤ x ≤ 4.
Answer
Explanation:
Step1: Recall average rate - of - change formula
The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a=-1$ and $b = 4$.
Step2: Calculate $h(a)$ and $h(b)$
First, find $h(-1)$: $h(-1)=(-1)^2-2\times(-1)-7=1 + 2-7=-4$. Then, find $h(4)$: $h(4)=4^2-2\times4-7=16-8 - 7=1$.
Step3: Calculate the average rate of change
Substitute $h(-1)=-4$ and $h(4)=1$ into the formula $\frac{h(4)-h(-1)}{4-(-1)}$. $\frac{1-(-4)}{4 + 1}=\frac{1 + 4}{5}=\frac{5}{5}=1$.
Answer:
$1$