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
