f(x) = max. (sin x , cos x ) for all x belongs to R . Then number of critical points belongs to ( -2pi , 2pi ) is/ are

(a) 5 (b) 4

(c) 7 (d) none of these

from the figure , we can see that there are 4 critical points.
in (-2π,-7π4) cosx>sinx,therefore f(x)=cosx in (-2π,-7π4)in (-7π4,-3π4); sinx>cosx, therefore f(x)=sinx in (-7π4,-3π4)in (-3π4,π4); cosx>sinx, therefore f(x)=cosx in (-3π4,π4)in (π4,5π4);sinx>cosx, therefore f(x)=sinx in (π4,5π4)in (5π4,2π); cosx>sinx, therefore f(x)=cosx in (5π4,2π)

thus the number of critical points are 4.
hope this helps you

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