Question

How do you find the average rate of change of `y=3x^2-3` over [-3,3]?

Answer 1

Zero

Explanation:

In general, the average rate of change of function `f(x)`, over an interval `[a,b], is`:

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

Here that means:

`([3(3)^2 - 3] - [3(-3)^2 - 3])/(3 - (- 3))`

`= (0)/(6) = 0`

This is hardly surprising as the function is even , ie `f(x) = f(-x)`.