已知函数f(x)=2sinx*cosx+2根号3cos^2x-根号3

已知:函数f(x)=2sinxcosx+2√3cos²x-√3
求:(1)单调增区间和最小正周期；
(2)当x∈[-π/4,π/4]时求最值.
f(x)=2sinxcosx+2√3cos²x-√3
=sin2x+√3cos2x
=2sin(2x+(π/3))
∵y=sinx的单调增区间是[2kπ-(π/2),2kπ+(π/2)],k∈Z；
∴2kπ-(π/2)≤2x+(π/3)≤2kπ+(π/2)
∴kπ-(5π/12)≤x≤kπ+(π/12)
(1)f(x)的单调增区间为[kπ-(5π/12),kπ+(π/12)]
f(x)的最小正周期T=2π/2=π
(2)x∈[-π/4,π/4]时,2x+(π/3)∈[-π/6,5π/6]
∴-1≤f(x)≤2,即f(x)min=-1,f(x)max=2