Answer with explanation:
The average rate of change for function f(x) over the interval a ≤ x ≤ b is given by :-
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
So, the rate of change for function [tex]f(x)=2x^2[/tex] over the interval −3 ≤ x ≤ 4 :
[tex]=\dfrac{2(4)^2-2(-3)^2}{4-(-3)}=\dfrac{14}{7}=2[/tex]
The rate of change for function [tex]g(x)=3x^2[/tex] over the interval −3 ≤ x ≤ 4 :
[tex]=\dfrac{3(4)^2-3(-3)^2}{4-(-3)}=\dfrac{21}{7}=3[/tex]
So, the rate of change for g(x) is greater than f(x) over the interval −3 ≤ x ≤ 4.
