Question

How do you find the average rate of change of `y=2x^2+2x+2` over [0,1/2]?

Answer 1

The average rate of change of a function `y` on the interval `[a,b]` is given by:

`(y(b)-y(a))/(b-a)`

Here, note that:

`y(0)=0+0+2=2`

`y(1/2)=2(1/4)+2(1/2)+2=7/2`

Then the rate of change is:

`(y(1/2)-y(0))/(1/2-0)=(7/2-2)/(1/2)=2(7/2-2)=3`