Question

The function f(t)=3t2.

(a) What is the average rate of change of f(t) between t=1 and t=1.001?
(b) What is the average rate of change of f(t) between t=2 and t=2.001?
(c) What is the average rate of change of f(t) between t=3 and t=3.001?
(d) What is the average rate of change of f(t) between t=4 and t=4.001?

Answer 1

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Answer 2

Since, for a function f(x),

`\text{Average rate of change between }x_1\text{ and }x_2=(f(x_2)-f(x_1))/(x_2-x_1)`

Given function,

`f(t)=3t^2`

Thus,

(a) the average rate of change of f(t) between t=1 and t=1.001

`=(f(1.001)-f(1))/(1.001-1)`

`=(3(1.001)^2-3(1)^2)/(0.001)`

`=6.003`

(b) the average rate of change of f(t) between t=2 and t=2.001

`=(f(2.001)-f(2))/(2.001-2)`

`=(3(2.001)^2-3(2)^2)/(0.001)`

`=12.003`

(c) the average rate of change of f(t) between t=3 and t=3.001

`=(f(3.001)-f(3))/(3.001-3)`

`=(3(3.001)^2-3(3)^2)/(0.001)`

`=18.003`

(d) the average rate of change of f(t) between t=4 and t=4.001

`=(f(4.001)-f(4))/(4.001-4)`

`=(3(4.001)^2-3(4)^2)/(0.001)`

`=24.003`

`=6.003`