given the function $h(x)=x^{2}+3x - 1$, determine the average rate of change of the function over the…
given the function $h(x)=x^{2}+3x - 1$, determine the average rate of change of the function over the interval $-7leq xleq5$.
Answer
Answer:
1
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, $a=-7$, $b = 5$.
Step2: Calculate $h(-7)$
Substitute $x=-7$ into $h(x)=x^{2}+3x - 1$. $h(-7)=(-7)^{2}+3\times(-7)-1=49-21 - 1=27$.
Step3: Calculate $h(5)$
Substitute $x = 5$ into $h(x)=x^{2}+3x - 1$. $h(5)=5^{2}+3\times5-1=25 + 15-1=39$.
Step4: Calculate the average rate of change
$\frac{h(5)-h(-7)}{5-(-7)}=\frac{39 - 27}{5 + 7}=\frac{12}{12}=1$.