Given the function h(x) = 4x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3. Part A: Find the average rate of change of each section. (4 points) Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

Average rate of change in Section A:

[tex]\dfrac{h(1)-h(0)}{1-0}=\dfrac{4-0}{1-0}=4[/tex]

Average rate of change in Section B:

[tex]\dfrac{h(3)-h(2)}{3-2}=\dfrac{12-8}{3-2}=4[/tex]

As you can see, the average rates of change are the same, as expected. [tex]h(x)=4x[/tex] is linear, which means it has a constant rate of change over any interval in its domain.