【数学】已知函数f(x)=2cosxsin(x+π/3)-√3sin^2(x)+sinxcosx

f(x)=2cosx*[sinx*(1/2)+cosx*(√3/2)]-√3sin^2 x+sinxcosx
=sinxcosx+√3cos^2 x-√3sin^2 x+sinxcosx
=2sinxcox+√3(cos^2 x-sin^2 x)
=sin2x+√3cos2x
=2sin[2x+(π/3)]
所以：
①最小正周期T=2π/2=π
②最大值=2,最小值=-2
③递增区间为2x+(π/3)∈[2kπ-(π/2),2kπ+(π/2)]
===> 2x∈[2kπ-(5π/6),2kπ+(π/6)]
===> x∈[kπ-(5π/12),kπ+(π/12)]（k∈Z）
④f(x)=x/(50π)
根的个数就相当于f(x)=2sin[2x+(π/3)]与直线g(x)=x/(50π)的交点的个数
f(x)周期为π,且在每一个周期内,f(x)与g(x)的交点个数为2
所以,一共有100个根