Question

How do you find the average rate of change of `f(x)=cot x` over the interval [pi/6, pi/2]?

Answer 1

`-9/(pisqrt(3))`

Explanation:

The average rate of change of a function over the closed interval `[a,b]` is given by:

`(f(b)-f(a))/(b-a)`

Here, `f=cotx,a=pi/6,b=pi/2`

Inputting:

`(cot(pi/2)-cot(pi/6))/(pi/2-pi/6)`

`(0-3/sqrt(3))/(pi/3)`

`(-3/sqrt(3))/(pi/3)`

`-9/(pisqrt(3))`

The graph helps us understand the above:

graph{cotx [-3.408, 4.387, -1.574, 2.32]}