For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g (x) = 1.8x2?

The average rate of change of g (x) = 1.8x² with interval 1 < x < 5 is 10.8

Step-by-step explanation:

Given

g (x) = 1.8x²

Interval 1 < x < 5

The average rate of change of the function g (x) on the interval [a, b] is calculated using the following formula:

Average Rate of change = (g (b) - g (a)) / (b - a)

Where a and b are values from the interval.

a = lower Interval = 1

b = upper Interval = 5

First, we need to calculate g (b) and g (a)

Given that g (x) = 1.8x²

g (a) = g (5) = 1.8 * 1²

g (a) = 1.8 * 1

g (a) = 1.8

Then we calculate g (a)

g (b) = g (5) = 1.8 * 5²

g (b) = 1.8 * 25

g (b) = 45

We then calculated the average Rate of change by substituting values in = (g (b) - g (a)) / (b - a)

Average Rate of Change = (45 - 1.8) / (5 - 1)

Average Rate of Change = 43.2/4

Average Rate of Change = 10.8

Hence, the average rate of change of g (x) = 1.8x² with interval 1 < x < 5 is 10.8