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 :-

$\dfrac{f(b)-f(a)}{b-a}$

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

$=\dfrac{2(4)^2-2(-3)^2}{4-(-3)}=\dfrac{14}{7}=2$

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

$=\dfrac{3(4)^2-3(-3)^2}{4-(-3)}=\dfrac{21}{7}=3$

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