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Sindrei [870]
3 years ago
8

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

Mathematics
1 answer:
babymother [125]3 years ago
3 0

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:

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=\frac{y_2-y_1}{x_2-x_1}

Calculate the slope:

m=\frac{-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.

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