已知函数f(x)=sin(wx+π/3)(w>0)f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)内,有最小值,无最大值,则w=()

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已知函数f(x)=sin(wx+π/3)(w>0)f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)内,有最小值,无最大值,则w=()

已知函数f(x)=sin(wx+π/3)(w>0)f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)内,有最小值,无最大值,则w=()
已知函数f(x)=sin(wx+π/3)(w>0)f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)内,
有最小值,无最大值,则w=()

已知函数f(x)=sin(wx+π/3)(w>0)f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)内,有最小值,无最大值,则w=()

f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)内有最小值,无最大值,
∴ 对称轴是x=π/4,且x=π/4时,y有最小值.
∴ w*(π/4)+π/3=2kπ-π/2
∴3w+4=24k-6
即 3w=24-10
∴ w=8k-10/3
且周期T≥(π/3-π/6)*2
即T≥π/12
即 2π/w≥π/12
∴ w≤24
∴ w=8-10/3=14/3 或w=16-10/3=38/3或w=24-10/3=62/3