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=()](/uploads/image/z/13578278-14-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dsin%EF%BC%88wx%2B%CF%80%2F3%EF%BC%89%EF%BC%88w%EF%BC%9E0%EF%BC%89f%EF%BC%88%CF%80%2F6%EF%BC%89%3Df%EF%BC%88%CF%80%2F3%EF%BC%89%2C%E4%B8%94f%EF%BC%88x%EF%BC%89%E5%9C%A8%E5%8C%BA%E9%97%B4%EF%BC%88%CF%80%2F6%2C%CF%80%2F3%EF%BC%89%E5%86%85%2C%E6%9C%89%E6%9C%80%E5%B0%8F%E5%80%BC%2C%E6%97%A0%E6%9C%80%E5%A4%A7%E5%80%BC%2C%E5%88%99w%3D%EF%BC%88%EF%BC%89)
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
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