已知函数f(x)=sin2x-2√3cos平方x+√3+a (1)求函数单调递减区间 (2)设x∈

2025-06-26 16:23:38
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回答1:

f(x) = sin2x-2√3cos平方x+√3+a

= sin2x-√3cos2x+a
= 2sin(2x-π/6)+a

2x-π/6属于(2kπ+π/2,2kπ+3π/2)时单调减
∴单调减区间:x属于((kπ+π/3,kπ+5π/6)

x∈[0,π/2]
2x∈[0,π]
2x-π/6∈[-π/6,5π/6]
2x-π/6=-π/6时,最小值 = 2*(-1/2)+a=-1+a=-2
a=-1
2x-π/6=π/2时,最大值 = 2*1-1= 1