Question

68. Find the average rate of change of f(x) = – 3x^2 + 5 from 3 to 7Number 68 on picture

Answer 1

So, we want to find the average rate of change of:

`f(x)=-3x^2+5`

From 3 to 7.

First, remember that the average rate of change of a function f(x) from a to b, can be found using the following formula:

`A=(f(b)-f(a))/(b-a)`

Where:

f(b) is the value of the function at the point b.

f(a) is the value of the function at the point a.

b is the final point

a is the initial point.

In our problem, we're given that:

`\begin{gathered} a=3 \\ b=7 \\ f(a)=-3(3)^2+5\to-3(9)+5\to-27+5=-22 \\ f(b)=-3(7)^2+5\to-147+5\to-142 \end{gathered}`

Now, let's just replace these values in the previous formula:

`A=(-142-(-22))/(7-3)=(-142+22)/(4)=(-120)/(4)=-30`

Therefore, the average rate of change is -30.

exercise:

Find the average rate of change of f(x):

`f(x)=-2x^2+1`

From 4 to 6.