Max f(x)=sqrt2 when x=(5pi)/4+k2pi or x=-(3pi)/4+k2pi
Min f(x)=-sqrt2 when x=pi/4+k2pi
Explanation:
f(x)=-sin x-cosx f(x)=-(sinx-six(pi/2-x)) f(x)=-2sin(pi/4)*cos(x-pi/4) f(x)=-sqrt2*cos(x-pi/4)
max f(x) when cos(x-pi/4)=-1
Min f(x) when cos(x-pi/4)=-1