Is #f(x)=cotx*tanx# increasing or decreasing at #x=pi/3#?

1 Answer
Jim H
Nov 22, 2015

Neither. #f(x)# is a constant function on its domain.

Explanation:

#cotx = 1/tanx#, so for every #x# for which both #tanx# and #cotx# are defined, we have #cotx tanx = 1#

So for all #x# except #pi/2k# where #k# is an integer, we get #f(x)=1# so #f# is neither increasing nor decreasing on any interval.

I don't know what definition you've been given for #f# is increasing at a point, but I cannot imagine a definition that would allow a constant function to be increasing at any point.

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