f(x)=(sin2x+1)e^(-2x)f'(x)=(sin2x+1)'e^(-2x)+(sin2x+1)[e^(-2x)]'=2cos2x *e^(-2x)+(sin2x+1)[-2e^(-2x)]=(2cos2x-2sin2x-2)*e^(-2x)=2[√2 cos(2x+π/4)-1]*e^(-2x)f'(0)=0