How do you find the average rate of change for the function #s(t)=4.5t^2# on the indicated intervals [6,12]?

Question

Evelyn Agard · Accepted Answer

Average Rate of Change = 81

Average rate of change of a function is can be found using the same method as finding the slope of linear function which is; #m=(y_2-y_1)/(x_2-x_1)# Therefore, this function's average rate of change is #Deltas(t)=(s(12)-s(6))/(12-6)=(648-162)/(12-6)=81# I hope this is helpful.

Aurora Alvarado · Answer

undefined To find the average rate of change of the function $ s(t) = 4.5t^2 $ on the interval $[6, 12]$, you calculate the difference in the function values at the endpoints of the interval and divide by the difference in the input values.

First, find the function values at the endpoints:
$ s(6) = 4.5(6)^2 = 162 $
$ s(12) = 4.5(12)^2 = 648 $

Next, calculate the difference in function values:
$ 648 - 162 = 486 $

Then, calculate the difference in input values:
$ 12 - 6 = 6 $

Finally, divide the difference in function values by the difference in input values to find the average rate of change:
$ \frac{486}{6} = 81 $

So, the average rate of change of the function $ s(t) = 4.5t^2 $ on the interval $[6, 12]$ is $ 81 $.