Question

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?

Answer 1

Answer:

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