f(x)=2（sin2x+√3/2）cosx-sin3x=2sin2xcosx+√3cosx-sin3x=sin3x+sinx+√3cosx-sin3x=2sin(x+π/3)∴x+π/3=2kπ+π/2,k∈Z, x=2kπ+π/6,k∈Z,f(x)max=2x+π/3=2kπ-π/2,x=2kπ-5π/6,k∈Z,f(x)min=-2...