Question

URGANT

Find the average rate of change of h(x)=−2xexponent2-2x from x=2 to x=6.
Simplify your answer as much as possible.

Answer 1

The average rate of change is -18.

Explanation:

We are given the function:

`\displaystyle h(x) = -2x^2 - 2x`

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:

`\displaystyle \begin{aligned} h(2) & = -2(2)^2 -2(2) \\ \\ & = -2(4)-4 \\ \\ & = -12\end{aligned}`

Likewise:

`\displaystyle \begin{aligned} h(6) &= -2(6)^2-2(6) \\ \\ & = -2(36) - 12 \\ \\ & = -84\end{aligned}`

The slope between the two endpoints is therefore:

`\displaystyle \begin{aligned} (\Delta y)/(\Delta x) & = ((-84)- (-12))/((6)-(2)) \\ \\ & = (-72)/(4) \\ \\ & = -18\end{aligned}`

In conclusion, the average rate of change of h from x = 2 to x = 6 is -18.