求证函数f(x)=(1-sina)(x3-2x2+x2+6),a属于(0,π/2)在区间(2/3,8/9)单调递减
问题描述：
求证函数f(x)=(1-sina)(x3-2x2+x2+6),a属于(0,π/2)在区间(2/3,8/9)单调递减
答
∵f'(x)=(1-sina)(3x^2-4x+1)
=3(1-sina)[x^2-(4x/3)+(1/3)]
=3(1-sina)[(x-2/3)^2-(1/9)]
f'(2/3)=-(1-sina)/3
∵a∈（0,π/2)
∴1-sina>0
∴f'(2/3)