函数f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)若x∈[0,π]求f(x)的最值

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函数f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)若x∈[0,π]求f(x)的最值函数f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(

函数f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)若x∈[0,π]求f(x)的最值
函数f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)若x∈[0,π]求f(x)的最值

函数f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)若x∈[0,π]求f(x)的最值

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f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)+sinx=√3sin(x+π/2)+sinx=2(√3/2cosx+1/2sinx)
=2sin(x+π/3)
x∈[0,π] π/3≤ x+π/3≤4π/3 -√3/2≤sin(x+π/3)≤1
-√3≤f(x)≤2