separate the interval [0,pi/2] f(x)=sinx^4+cosx^4 Share with your friends Share 0 Lovina Kansal answered this Dear student Correct question isSeparate the inerval 0,π2 into sub-intervals in which f(x)=sin4x+cos4xis increasing or decreasing.We have.f(x)=sin4x+cos4xf'(x)=4sin3x cosx-4cos3xsinx=-4sinx cosxcos2x-sin2x=-22sinx cosxcos2x=-2sin2x cos2x=-sin4xWe have,0<x<π2⇒0<4x<2πSince sine function is positive in the first quadrant and second quadrants andnegative in the third and fourth quadrans. So, we consider the following:Case1: Whne 0<4x<πIn this case, we havesin4x>0⇒-sin4x<0⇒f'(x)<0⇒f'(x)<0 for 0<4x<π i.e 0<x<π4So, f(x) is decreasing on 0,π4Case 2: When π<4x<2πIn this case, we havesin4x<0⇒-sin4x>0⇒f'(x)>0∴f'(x)>0 for π<4x<2π i.e., π4<x<π2So, f(x) is increasing on π4,π2 Regards -1 View Full Answer