函数y=Asin(ωx+φ)(x∈R,A>0,ω>0,φ的绝对值<π/2)的图像上相邻的最高点与最低点的坐标分别为M(5π/12,3),N(11π/12,-3)(1)求此函数的解析式(2)f(x)的单调增区间(3)f(x)的对称轴和对
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![函数y=Asin(ωx+φ)(x∈R,A>0,ω>0,φ的绝对值<π/2)的图像上相邻的最高点与最低点的坐标分别为M(5π/12,3),N(11π/12,-3)(1)求此函数的解析式(2)f(x)的单调增区间(3)f(x)的对称轴和对](/uploads/image/z/3011459-59-9.jpg?t=%E5%87%BD%E6%95%B0y%3DAsin%28%CF%89x%2B%CF%86%29%28x%E2%88%88R%2CA%EF%BC%9E0%2C%CF%89%EF%BC%9E0%2C%CF%86%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%EF%BC%9C%CF%80%2F2%29%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8A%E7%9B%B8%E9%82%BB%E7%9A%84%E6%9C%80%E9%AB%98%E7%82%B9%E4%B8%8E%E6%9C%80%E4%BD%8E%E7%82%B9%E7%9A%84%E5%9D%90%E6%A0%87%E5%88%86%E5%88%AB%E4%B8%BAM%285%CF%80%2F12%2C3%EF%BC%89%2CN%EF%BC%8811%CF%80%2F12%2C-3%EF%BC%89%EF%BC%881%EF%BC%89%E6%B1%82%E6%AD%A4%E5%87%BD%E6%95%B0%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%EF%BC%882%EF%BC%89f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%EF%BC%883%EF%BC%89f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E5%92%8C%E5%AF%B9)
函数y=Asin(ωx+φ)(x∈R,A>0,ω>0,φ的绝对值<π/2)的图像上相邻的最高点与最低点的坐标分别为M(5π/12,3),N(11π/12,-3)(1)求此函数的解析式(2)f(x)的单调增区间(3)f(x)的对称轴和对
函数y=Asin(ωx+φ)(x∈R,A>0,ω>0,φ的绝对值<π/2)的图像上相邻的最高点与最低点的坐标分别为M(5π/12,3),N(11π/12,-3)
(1)求此函数的解析式
(2)f(x)的单调增区间
(3)f(x)的对称轴和对称中心
(4)f(x)的最小值以及取得最小值时的x的集合
(1)(2)问只写答案,(3)(4)写过程
函数y=Asin(ωx+φ)(x∈R,A>0,ω>0,φ的绝对值<π/2)的图像上相邻的最高点与最低点的坐标分别为M(5π/12,3),N(11π/12,-3)(1)求此函数的解析式(2)f(x)的单调增区间(3)f(x)的对称轴和对
函数y=Asin(ωx+φ)(x∈R,A>0,ω>0,φ的绝对值<π/2)的图像上相邻的最高点与最低点的坐标分别为M(5π/12,3),N(11π/12,-3)
(1)求此函数的解析式
(2)f(x)的单调增区间
(3)f(x)的对称轴和对称中心
(4)f(x)的最小值以及取得最小值时的x的集合
(1)解析:∵函数f(x)=Asin(ωx+φ)(x∈R,A>0,ω>0,|φ|<π/2),
∴A=3,T/2=11π/12-5π/12=π/2==>T=π==>w=2
∴f(x)=3sin(2x+φ)==> f(5π/12)=sin(5π/6+φ)=1==>5π/6+φ=π/2==>φ=-π/3
∴f(x)=3sin(2x-π/3)
(2)解析:∵f(x)=3sin(2x-π/3),单调减区间为[5π/12,11π/12]
∴单调增区间为[kπ-π/12,kπ+5π/12]
(3)解析:∵f(x)=3sin(2x-π/3),
对称轴为kπ-π/12或kπ+5π/12
对称中心为kπ-π/3或kπ+π/6
(4)解析:∵f(x)=3sin(2x-π/3),
2x-π/3=2kπ-π/2==>x=kπ-π/12
f(x)的最小值为-3,取得最小值时x=kπ-π/12
(1) y=3sin(2x-π/3)
(2) [kπ-π/12,kπ+5π/12]
(3) sin对称轴为kπ+π/2 对称中心kπ 令2x-π/3分别等于上述值即可
(4) 最小值-3 令2x-π/3等于2kπ-π/2