已知函数y=sinwx在[-30°,60°]上是增函数,则w的取值范围是( )A.[-1.5,0) B.[-3,0) C.(0,1.5] D.(0,3]
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![已知函数y=sinwx在[-30°,60°]上是增函数,则w的取值范围是( )A.[-1.5,0) B.[-3,0) C.(0,1.5] D.(0,3]](/uploads/image/z/3971239-7-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0y%3Dsinwx%E5%9C%A8%5B-30%C2%B0%2C60%C2%B0%5D%E4%B8%8A%E6%98%AF%E5%A2%9E%E5%87%BD%E6%95%B0%2C%E5%88%99w%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%EF%BC%88+%EF%BC%89A.%5B-1.5%2C0%29+B.%5B-3%2C0%29+C.%280%2C1.5%5D+D.%280%2C3%5D)
已知函数y=sinwx在[-30°,60°]上是增函数,则w的取值范围是( )A.[-1.5,0) B.[-3,0) C.(0,1.5] D.(0,3]
已知函数y=sinwx在[-30°,60°]上是增函数,则w的取值范围是( )
A.[-1.5,0) B.[-3,0) C.(0,1.5] D.(0,3]
已知函数y=sinwx在[-30°,60°]上是增函数,则w的取值范围是( )A.[-1.5,0) B.[-3,0) C.(0,1.5] D.(0,3]
sin在-90到+90是增函数,且要求wx为增函数,所以w>0,所以wx<=90,而x<=60,则w<=1.5,选C.
sinwx的增区间是[-π/2w,+π/2w]
所以即为[-π/6,π/3]包含于[-π/2w,π/2w]
所以w>0,π/2w≥π/3,-π/2w≤-π/6
得w∈[-3,0)
sina的增区间是[2kπ-π/2,2kπ+π/2]
y=sinwx在[-30°,60°]上是增函数,说明,
当x=-30°时,-wπ/6∈[2kπ-π/2,2kπ+π/2],解得:w∈[-12k-3,-12k+3];
当x=-60°时,-wπ/3∈[2kπ-π/2,2kπ+π/2],解得:w∈[-6k-3/2,-6k+3/2];
又:-wπ/6<-wπ/3,解得:...
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sina的增区间是[2kπ-π/2,2kπ+π/2]
y=sinwx在[-30°,60°]上是增函数,说明,
当x=-30°时,-wπ/6∈[2kπ-π/2,2kπ+π/2],解得:w∈[-12k-3,-12k+3];
当x=-60°时,-wπ/3∈[2kπ-π/2,2kπ+π/2],解得:w∈[-6k-3/2,-6k+3/2];
又:-wπ/6<-wπ/3,解得:w<0
综上得:当k=0时,w∈(0,1.5]
所以答案选C
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