Question

How all work.

A) What is the average rate of change of the function g(x) = 14x + 6 over the interval [0, 5]?
B) What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval [0,5]?
C) How does this compare to your Answers for Problem 4?

Answer 1

Here we can only answer A and B.

For a given function f(x), the average rate of change in a given interval [a, b] is given by:

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

A) we have g(x) = 14*x + 6, and the interval [0, 5], the average rate of change is:

`r = (g(5) - g(0))/(5 - 0) = ((14*5 + 6) - (14*0 + 6))/(5) = (14*5)/(5) = 14`

The average rate of change is 14.

B) We have g(x) = 3*(2x) - 6

we can rewrite this as:

g(x) = 3*2*x - 6 = 6x - 6

And we want to find the rate of change in the interval [0, 5]

is:

`r = (g(5) - g(0))/(5 - 0) = ((6*5 - 6) - (6*0 - 6))/(5) = 6`