已知函数f(x)=sin(ωx+π/3),f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)有最小值无最大值,则ω=

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/19 06:57:24
已知函数f(x)=sin(ωx+π/3),f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)有最小值无最大值,则ω=
xQMJ@NSҦ%LN "r@Ԃ%T*VlL aP2t+80~3~!m0WݳB{LThg3 NW -٘?D>E &"F< scr&KvH|5{}ًTT_2 y],(.7I\XHŚylU,UYi-DM dC^gGB0(GϼAs}7/E9lե_IOzU>TRc+~|S4sұı~^fC

已知函数f(x)=sin(ωx+π/3),f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)有最小值无最大值,则ω=
已知函数f(x)=sin(ωx+π/3),f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)有最小值无最大值,则ω=

已知函数f(x)=sin(ωx+π/3),f(π/6)=f(π/3),且f(x)在区间(π/6,π/3)有最小值无最大值,则ω=
根据f(π/6)=f(π/3),以及正弦函数的性质,可知有一条对称轴为x=(π/6+π/3)/2=π/4
f(x)在区间(π/6,π/3)有最小值无最大值,则f(π/4)=-1,T≥π/3-π/6=π/6
同时T=2π/ω,这里我们一般考虑ω>0
所以0<ω≤12
sin(ω*π/4+π/3)=-1,故可得ω=14/3