Answer:
The average rate of change is -18.
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = -2x^2 - 2x[/tex]
And we want to find its average rate of change from x = 2 to x = 6.
Recall that to find the average rate of change between two points of any functions, we find the slope between the two endpoints. Hence, evaluate the endpoints:
[tex]\displaystyle \begin{aligned} h(2) & = -2(2)^2 -2(2) \\ \\ & = -2(4)-4 \\ \\ & = -12\end{aligned}[/tex]
Likewise:
[tex]\displaystyle \begin{aligned} h(6) &= -2(6)^2-2(6) \\ \\ & = -2(36) - 12 \\ \\ & = -84\end{aligned}[/tex]
The slope between the two endpoints is therefore:
[tex]\displaystyle \begin{aligned} \frac{\Delta y}{\Delta x} & = \frac{(-84)- (-12)}{(6)-(2)} \\ \\ & = \frac{-72}{4} \\ \\ & = -18\end{aligned}[/tex]
In conclusion, the average rate of change of h from x = 2 to x = 6 is -18.
