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

Asked by vaibhav gupta | 26th Sep, 2013, 06:20: PM

Expert Answer:

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
 
for increasing function
2npi-pi/2

Answered by  | 26th Sep, 2013, 10:07: PM

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