Question

I dont understand even where to begin on this, please help!​

Answer 1

-17

Explanation:

The average rate of change is synonymous to the slope of a function.

We want to find the average rate of change for the function:

`f(x)=-2x^2-3x-8`

For the interval [3, 4]

So, we simply have to calculate the values of the function at the endpoints and then find the slope between them.

Our endpoint values are x=3 and x=4. So:

`\begin{aligned} f(3)&=-2(3)^2-3(3)-8 \\ f(3)&=-18-9-8 \\ f(3)&=-35\end{aligned}`

And:

`\begin{aligned} f(4)&=-2(4)^2-3(4)-8 \\ f(4)&=-32-12-8 \\f(4)&=-52\end{aligned}`

So, we have the two points (3, -35) and (4, -52).

Now, we can use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Calculate the slope:

`m=(-52-(-35))/(4-3)=-17/1=-17`

Hence, the slope or the average rate of change for our function for the interval [3, 4] is -17.