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

 

 

……….(i)

Now  for all real  as . Also  > 0

(i)  is increasing if , i.e., from eq. (i), 

 lies in I and IV quadrants, i.e.,  is increasing for 

and 

and (ii)  is decreasing if , i.e., from eq. (i), 

  lies in II and III quadrants, i.e.,  is decreasing for