已知函数f(x)=2cosxsin(x+π/3)-根号下3(sinx)^2+sinxcosx
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已知函数f(x)=2cosxsin(x+π/3)-根号下3(sinx)^2+sinxcosx
求函数最大、最小值
求函数最大、最小值
f(x)=2cosx[1/2sinx+√3/2cosx]-√3sin^2(x)+sinxcosx
=sinxcosx+√3cos^2(x)-√3sin^2(x)+sinxcosx
=sin2x+√3cos2x
=2sin(2x+π/6)
当2x+π/6=π/2+2kπ时,即x=π/6+kπ时,f(x)取最大值,y(MAX) = 2
当2x+π/6=-π/2+2kπ时,即x= -π/3+kπ时,f(x)取最小值,y(min) = - 2
=sinxcosx+√3cos^2(x)-√3sin^2(x)+sinxcosx
=sin2x+√3cos2x
=2sin(2x+π/6)
当2x+π/6=π/2+2kπ时,即x=π/6+kπ时,f(x)取最大值,y(MAX) = 2
当2x+π/6=-π/2+2kπ时,即x= -π/3+kπ时,f(x)取最小值,y(min) = - 2
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