given the function $h(x)=-x^{2}+8x + 20$, determine the average rate of change of the function over the…
given the function $h(x)=-x^{2}+8x + 20$, determine the average rate of change of the function over the interval $0leq xleq5$.
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 $\frac{h(b)-h(a)}{b - a}$, where $a = 0$ and $b = 5$.
Step2: Calculate $h(0)$
Substitute $x = 0$ into $h(x)=-x^{2}+8x + 20$. $h(0)=-(0)^{2}+8(0)+20=20$.
Step3: Calculate $h(5)$
Substitute $x = 5$ into $h(x)=-x^{2}+8x + 20$. $h(5)=-(5)^{2}+8(5)+20=-25 + 40+20=35$.
Step4: Calculate the average rate of change
Use the formula $\frac{h(5)-h(0)}{5 - 0}$. $\frac{35 - 20}{5}=\frac{15}{5}=3$.
Answer:
$3$