高一数学,可加分,在线等已知ω∈R+且函数f(x)=sinωx在区间[-π/3,π/4]上单调递增,则ω的取值范围是答案是（0,3/2],求过程

Question

高一数学,可加分,在线等
已知ω∈R+且函数f(x)=sinωx在区间[-π/3,π/4]上单调递增,则ω的取值范围是_____
答案是（0,3/2],求过程

Answer 1

求f(x)=sinωx包含0的增区间
即-π/2≤ωx≤π/2
∴ -π/(2ω)≤x≤π/(2ω)
即增区间是【-π/(2ω),π/(2ω)】
要在[-π/3,π/4]上单调递增
则【-π/(2ω),π/(2ω)】包含[-π/3,π/4]
∴ -π/(2ω)≤-π/3且π/(2ω)≥π/4
∴ 2ω≤3且2ω≤4
∴ ω≤3/2且ω≤2
又ω>0
∴ 0