若x=π/6是函數(shù)f(x)=根號(hào)3sinwx+coswx圖像的一條對(duì)稱軸,當(dāng)w取最小正數(shù)時(shí),函數(shù)的單調(diào)遞增,遞減區(qū)間
解析：∵x=π/6是函數(shù)f(x)=根號(hào)3sinwx+coswx圖像的一條對(duì)稱軸
f(x)=根號(hào)3sinwx+coswx=2sin(wx+π/6)
wx+π/6=2kπ-π/2==>x=2kπ/w-2π/(3w)
令-2π/(3w)=π/6==>w=-4
wx+π/6=2kπ+π/2==>x=2kπ/w+π/(3w)
令π/(3w)=π/6==>w=2
∵w取最小正數(shù)
∴f(x)=2sin(2x+π/6)
2kπ-π/2