Question

How do you find the average rate of change of `f(x)=cot x` over the interval [pi/4, 3pi/4]?

Answer 1

The average rate of change of `f(x)` is `-1.27(2dp)`

Explanation:

`f(x) =cotx`

The average rate of change of a function from `x=pi/4` to

`x=(3pi)/4` is `(f((3pi)/4)-f(pi/4))/((3pi)/4-pi/4)`

`f((3pi)/4) = cot ((3pi)/4)= -1 and f((pi)/4) = cot(pi/4)= 1`

`:. (f((3pi)/4)-f(pi/4))/((3pi)/4-pi/4) = (-1-1)/((3pi)/4-pi/4)`

`=-2/(pi/2) = -4/pi ~~ -1.27(2dp)`

The average rate of change of `f(x)` is `-1.27(2dp)` [Ans]