Question
Thu September 26, 2013 By: Vaibhav Gupta
 

Find the intervals in which the function f given by f(x)=(4sinx-2x-xcosx)/(2+cosx) is (i)strictly increasing (ii)strictly decreasing.

Expert Reply
Thu September 26, 2013
f(x)=(4sinx -2x-xcosx)/(2+cosx)
diff w.r. to x we will get
f?(x)=(4cosx-cos^2 x)/(2+cosx)^2
or
f'(x)=cosx(4-cosx)/(2+cosx)^2
as we know that
4-cosx>0
so for decreasing function
cosx<0
or
2npi+pi/2<x<2npi+3pi/2 where n?N
 
for increasing function
2npi-pi/2<x<2npi+pi/2 where n?N
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