已知函数f(x)=asinxcosx-根号3acos2x+根号3a/2+b(a＞0)

先化简啊。

(x)=asin2x/2-√3a(cos2x+1)/2+√3a/2+b
=asin(2x-π/3)+b
a>0,所以f(x)递减区间和sin一样
所以2kπ+π/2<2x-π/3<2kπ+3π/2
2kπ+5π/6<2x<2kπ+11π/6
kπ+5π/12<x<kπ+11π/12
所以递减区间(kπ+5π/12,kπ+11π/12),k是整数

0<=x<=π/2
-π/3<=2x-π/3<=2π/3
所以-√3/2<=sin(2x-π/3)<=1
所以最大=a+b=√3
最小=-√3a/2+b=-2
a=2,b=√3-2