f(x) = max (sin x , cos x ) for all x belongs to R Then number - Maths - Continuity and Differentiability

Question

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

Ajanta Trivedi · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/pic07_3_1%20png"
style="width: 650px; height: 400px;">
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

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

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