# How do you find the average rate of change of #f(t) = 1.1t^2 - 2.5t + 1.5# over the interval [3,5]?

6.3

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To find the average rate of change of the function f(t) = 1.1t^2 - 2.5t + 1.5 over the interval [3,5], we use the formula:

Average rate of change = (f(b) - f(a)) / (b - a)

where 'a' and 'b' represent the endpoints of the interval.

- Substitute t = 3 and t = 5 into the function to find f(3) and f(5).
- Calculate the difference between f(5) and f(3).
- Divide the difference by the length of the interval, which is (5 - 3).

Let's calculate it:

- Find f(3):

f(3) = 1.1(3)^2 - 2.5(3) + 1.5 = 1.1(9) - 7.5 + 1.5 = 9.9 - 7.5 + 1.5 = 3.9

- Find f(5):

f(5) = 1.1(5)^2 - 2.5(5) + 1.5 = 1.1(25) - 12.5 + 1.5 = 27.5 - 12.5 + 1.5 = 16.5

- Calculate the difference:

f(5) - f(3) = 16.5 - 3.9 = 12.6

- Calculate the average rate of change:

Average rate of change = (f(5) - f(3)) / (5 - 3) = 12.6 / 2 = 6.3

So, the average rate of change of f(t) over the interval [3,5] is 6.3.

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