Compare the average rate of change from 0 to 1/6...

Question

f (x)=x

g (x)=x^2

h(x)=x^3

Answer 1

Average rate of change is the slope of the line joining the first and last values of each function.

 

at x=0:       f(x) = 0,         g(x) = 0,               h(x) = 0

at x=1/6:    f(x) = 1/6       g(x) = 1/36,          h(x) = 1/216

 

Slope (average rate of change) = change in Y (the function) divided by the change in x

   The change in x in all cases is 1/6  - 0  =  1/6

 

The average rate of change for f(x)  is  1/36

The average rate of change for g(x) is  1/216

The average rate of change for h(x) is  1/1216