已知函数f(x)=sin(wx+π/3) (w>0) 若f(π/6)=f(π/3),闭区间【π/6,π/3】内有最大值,无最小值,则w取
问题描述:
已知函数f(x)=sin(wx+π/3) (w>0) 若f(π/6)=f(π/3),闭区间【π/6,π/3】内有最大值,无最小值,则w取
答
解由f(π/6)=f(π/3),且f(x)在区间【π/6,π/3】内有最大值,知函数的对称轴为x=π/4故当x=π/4,知f(π/4)=sin(wπ/4+π/3)=1即wπ/4+π/3=2kπ+π/2,k属于Z解得w=8k+2/3,k属于Z又由w>0知当k=0时,w=2/3.当让此题还有...