Question

question given the function $h(x)=-x^{2}-5x + 11$, determine the average rate of change of the function over the interval $-8leq xleq4$.

Explanation:

Step1: Find h(-8) and h(4)

$h(-8)=-(-8)^2 - 5\times(-8)+11=-64 + 40+11=-13$
$h(4)=-(4)^2-5\times4 + 11=-16-20 + 11=-25$

Step2: Calculate average rate of change

$\frac{h(4)-h(-8)}{4-(-8)}=\frac{-25-(-13)}{4 + 8}=\frac{-12}{12}=-1$

Answer:

-1