Question

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

Answer 1

Answer:

See answer below

Step-by-step explanation:

Hi there,

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

$Rate_{avg} = \frac{f(b)-f(a)}{b-a}$

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:

$f(2)-f(0)= \frac{1}{4} (2^{2} -0^{2} ) = 1 \\g(2)-g(0)= 5(2-0)= 10\\h(2)-h(0)= 2^{2} - 0^{2} =4$

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,