Question

How do you find the average rate of change of `f(t)= 2t + 7` from [1,2]?

Answer 1

`2`

Explanation:

All you need to find is `(f(2)-f(1))/(2-1)`.

Here's a "cheat": the rate of change for a line is constant--it's the slope. Thus the average rate of change on any interval where your function is a line should always result in the slope.

Here, we get `(f(2)-f(1))/(2-1)=(11-9)/(2-1)=2/1=2` which is the slope of `2t+7`, as expected.