Question

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)

Answer 1

Answer with explanation:

The average rate of change in a function f(x) from x=a to x=b is given by :-

`k=(f(b)-f(a))/(b-a)`

For Section A .

The average rate of change in a function h(x)=4x from x=0 to x=1 is given by :-

`k=(h(1)-h(0))/(1-0)\\\\=(4-0)/(1)=4`

For section B .

The average rate of change in a function h(x)=4x from x=2 to x=3 is given by :-

`k=(h(3)-h(2))/(3-2)\\\\=(12-8)/(1)=4`

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.