Answer with explanation:
The average rate of change in a function f(x) from x=a to x=b is given by :-
[tex]k=\dfrac{f(b)-f(a)}{b-a}[/tex]
For Section A .
The average rate of change in a function h(x)=4x from x=0 to x=1 is given by :-
[tex]k=\dfrac{h(1)-h(0)}{1-0}\\\\=\dfrac{4-0}{1}=4[/tex]
For section B .
The average rate of change in a function h(x)=4x from x=2 to x=3 is given by :-
[tex]k=\dfrac{h(3)-h(2)}{3-2}\\\\=\dfrac{12-8}{1}=4[/tex]
The average rate of section A is same for section B because the function is a linear function, and the rate of change of a linear function is constant.
