Question

Which function below would have the smallest Average rate of change From X =0 to x=2

Answer 1

See answer below

Explanation:

Hi there,

To get started, recall the average rate of change formula (essentially the same thing as slope):

`Rate_(avg) = (f(b)-f(a))/(b-a)`

So, just determine the average rate for each function between points [0,2] (a and b for the formula above, respectively).

To make it less time consuming, you do not need to do the division portion as it is same for all of them and (2-0) is greater than 1:

`f(2)-f(0)= (1)/(4) (2^(2) -0^(2) ) = 1 \\g(2)-g(0)= 5(2-0)= 10\\h(2)-h(0)= 2^(2) - 0^(2) =4`

Without even doing the divison of (b-a), we can already see that the function with smallest average rate of change between [0,2] is f(x).

thanks,