Answer:
The average rate of change is -3.
Step-by-step explanation:
We are given the function:
[tex]f(x)=9-x^2[/tex]
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:
[tex]f(0)=9-(0)^2=9[/tex]
So, our first point is (0, 9).
For our second endpoint at x = 3, our function evaluates to :
[tex]f(x)=9-(3)^2=0[/tex]
So, our second point is (3, 0).
Then by the slope formula, our average rate of change will be:
[tex]\displaystyle m=\frac{0-9}{3-0}=\frac{-9}{3}=-3[/tex]
