设函数f(x)=2根号3sinxcosx,求f(x)的最大值,最小正周期和单调区间

利用二倍角公式:sin2x=2sinxcosc∴f(x)=2√3sinxcosx=√3sin2x∵-1≤sin2x≤1∴-√3≤f(x)≤√3∴f(x)max=√3最小正周期:T=2π/2=π单调区间：当-π/2+2kπ≤2x≤π/2+2kπ时即:-π/4+kπ≤x≤π/4+kπ时f(x)单调递...