Answer:
-17
Step-by-step 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:
[tex]f(x)=-2x^2-3x-8[/tex]
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:
[tex]\begin{aligned} f(3)&=-2(3)^2-3(3)-8 \\ f(3)&=-18-9-8 \\ f(3)&=-35\end{aligned}[/tex]
And:
[tex]\begin{aligned} f(4)&=-2(4)^2-3(4)-8 \\ f(4)&=-32-12-8 \\f(4)&=-52\end{aligned}[/tex]
So, we have the two points (3, -35) and (4, -52).
Now, we can use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Calculate the slope:
[tex]m=\frac{-52-(-35)}{4-3}=-17/1=-17[/tex]
Hence, the slope or the average rate of change for our function for the interval [3, 4] is -17.
