Question

How do the average rates of change for the functions f(x) = 2x2 and g(x) = 3x2 over the interval −3 ≤ x ≤ 4 compare?

Answer 1

Answer with explanation:

The average rate of change for function f(x) over the interval a ≤ x ≤ b is given by :-

`(f(b)-f(a))/(b-a)`

So, the rate of change for function
`f(x)=2x^2` over the interval −3 ≤ x ≤ 4 :

`=(2(4)^2-2(-3)^2)/(4-(-3))=(14)/(7)=2`

The rate of change for function
`g(x)=3x^2` over the interval −3 ≤ x ≤ 4 :

`=(3(4)^2-3(-3)^2)/(4-(-3))=(21)/(7)=3`

So, the rate of change for g(x) is greater than f(x) over the interval −3 ≤ x ≤ 4.