Question

How do you find the average rate of change for f(x)=9-x^2 between two points: x=0 to x=3?

Answer 1

Answer:

The average rate of change is -3.

Step-by-step explanation:

We are given the function:

$f(x)=9-x^2$

And we want to find the average rate of change from x = 0 to x = 3.

In other words, we will compute the function at the two endpoints, and then find the slope of the line that crosses the two points.

For our first endpoint at x = 0, our function evaluates to:

$f(0)=9-(0)^2=9$

So, our first point is (0, 9).

For our second endpoint at x = 3, our function evaluates to :

$f(x)=9-(3)^2=0$

So, our second point is (3, 0).

Then by the slope formula, our average rate of change will be:

$\displaystyle m=\frac{0-9}{3-0}=\frac{-9}{3}=-3$