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

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Answer 1 · 2017-11-29T12:42:38

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

#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]