Question

How do you find the average rate of change of `y=1/2x^2` over [-2,6]?

Answer 1

`"Average rate of change"=2`

Explanation:

Average rate of change over the interval `[a,b]` for `y=f(x)` is given by `(f(b)-f(a))/(b-a)`

Hence, average rate of change of from `x=-2` to `x=6` i.e. over the interval `[-2,6]` for `y=f(x)=1/2x^2` is given by

`"Average rate of change"=(f(6)-f(-2))/(6-(-2))`

As `f(-2)=1/2(-2)^2=2` and `f(6)=1/2(6)^2=18`

`"Average rate of change"=(18-2)/8=16/2=2`