given the function g(x)= -x² - 4x + 9, determine the average rate of change of the function over the…
given the function g(x)= -x² - 4x + 9, determine the average rate of change of the function over the interval -8 ≤ x ≤ 0.
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-8$ and $b = 0$.
Step2: Calculate $g(-8)$
Substitute $x=-8$ into $g(x)=-x^{2}-4x + 9$. $g(-8)=-(-8)^{2}-4\times(-8)+9=-64 + 32+9=-23$.
Step3: Calculate $g(0)$
Substitute $x = 0$ into $g(x)=-x^{2}-4x + 9$. $g(0)=-(0)^{2}-4\times(0)+9=9$.
Step4: Calculate the average rate of change
Use the formula $\frac{g(0)-g(-8)}{0-(-8)}$. $\frac{9-(-23)}{8}=\frac{9 + 23}{8}=\frac{32}{8}=4$.
Answer:
4