函数y=根号3×sinx+cosx,x∈[-π/2,π/2]的最大值为多少？

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y=根号3×sinx+cosx
=2[(√3/则冲态判大2)sinx+(1/2)cosx]
=2sin(x+π/6)
因x∈[-π/2,π/2]
x+π/6∈[-π/3,2π/3]
所以sin(x+π/6)=1
y最孙源大=2

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