Question

question
given the function $g(x)=-x^{2}+2x + 8$, determine the average rate of change of the function over the interval $-3leq xleq3$.

Explanation:

Step1: Find function values at endpoints

$g(-3)=-(-3)^2 + 2(-3)+8=-9 - 6 + 8=-7$
$g(3)=-3^2 + 2\times3 + 8=-9+6 + 8=5$

Step2: Calculate average rate of change

$\frac{g(3)-g(-3)}{3-(-3)}=\frac{5 - (-7)}{6}=\frac{12}{6}=2$

Answer:

2