given the function $g(x)=-x^{2}+3x + 5$, determine the average rate of change of the function over the…
given the function $g(x)=-x^{2}+3x + 5$, determine the average rate of change of the function over the interval $-4leq xleq6$.
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, $a=-4$ and $b = 6$.
Step2: Calculate $g(a)$
Substitute $x=-4$ into $g(x)=-x^{2}+3x + 5$. $g(-4)=-(-4)^{2}+3\times(-4)+5=-16-12 + 5=-23$.
Step3: Calculate $g(b)$
Substitute $x = 6$ into $g(x)=-x^{2}+3x + 5$. $g(6)=-6^{2}+3\times6+5=-36 + 18+5=-13$.
Step4: Calculate average rate of change
Use the formula $\frac{g(b)-g(a)}{b - a}=\frac{-13-(-23)}{6-(-4)}=\frac{-13 + 23}{6 + 4}=\frac{10}{10}=1$.
Answer:
$1$