函数f(x,θ)=
|
∵x>2,
∴x-1-sinθ>0,
而f(x,θ)=
=x2-x-xsinθ+8 x-1-sinθ
=x+x(x-1-sinθ)+8 x-1-sinθ
=x-1-sinθ+8 x-1-sinθ
+1+sinθ≥28 x-1-sinθ
+1+sinθ,(x-1-sinθ)• 8 x-1-sinθ
当且仅当x-1-sinθ=
即x-1-sinθ=28 x-1-sinθ
此时x=1+22
+sinθ取等号;2
而sinθ∈[-1,1],
∴当sinθ=-1,x=2
时,函数f(x,θ)=2
(x>2)取最小值为4x2-x-xsinθ+8 x-1-sinθ
.2
故选A.