若函数f(X)=sinωx(ω>0)在区间[0,π/3]上单调递增,在区间[π/3,π/2]上单调递减,则ω=多少
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![若函数f(X)=sinωx(ω>0)在区间[0,π/3]上单调递增,在区间[π/3,π/2]上单调递减,则ω=多少](/uploads/image/z/3857235-51-5.jpg?t=%E8%8B%A5%E5%87%BD%E6%95%B0f%EF%BC%88X%29%3Dsin%CF%89x%28%CF%89%3E0%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5B0%2C%CF%80%2F3%5D%E4%B8%8A%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%2C%E5%9C%A8%E5%8C%BA%E9%97%B4%5B%CF%80%2F3%2C%CF%80%2F2%5D%E4%B8%8A%E5%8D%95%E8%B0%83%E9%80%92%E5%87%8F%2C%E5%88%99%CF%89%3D%E5%A4%9A%E5%B0%91)
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若函数f(X)=sinωx(ω>0)在区间[0,π/3]上单调递增,在区间[π/3,π/2]上单调递减,则ω=多少
若函数f(X)=sinωx(ω>0)在区间[0,π/3]上单调递增,在区间[π/3,π/2]上单调递减,则ω=多少
若函数f(X)=sinωx(ω>0)在区间[0,π/3]上单调递增,在区间[π/3,π/2]上单调递减,则ω=多少
sinωx,相对于sinx,最大值不变,增减性不变,变的只是增减区间
由题画图,可得
[0,π/3]是单调递增区间,π/3是第一个最大值点,区间对应sinx的[0,π/2]
f(0)=sin0=0
f(π/3)=sin(π/2)=1
ω=3/2