Given the function f(x) = 5x, 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. 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.

The average rate is given by

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

Section A

a = 0
b = 1

f(x) = 5.x

f(a) = 5.0 = 0
f(b) = 5.1 = 5

Then 

5 - 0 / 1 - 0 = 5/1 = 5

Section B

a = 2
b = 3

f(a) = 5.2 = 10
f(b) = 5.3 = 15

15-10 / 3 - 2 = 5 

Since, f(x) is a linear equation with slope = 5, its rate of change is constant. Thus, both rates (Section A & B) are equal to 5.