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

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Answer 1 · 2018-03-01T12:42:06

#-9/(pisqrt(3))#

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]}