设w>0,若函数f(x)=sinwx在区间[-π/5,π/5]上是增函数,求w的取值范围.

问题描述:

设w>0,若函数f(x)=sinwx在区间[-π/5,π/5]上是增函数,求w的取值范围.

f(x)=sinwx是奇函数,图象关于原点对称由-π/2≤wx≤π/2 ==> -π/(2w)≤x≤π/(2w)∴f(x)在原点附近单调递增区间为[-π/(2w),π/(2w)]f(x)=sinwx在区间[-π/5,π/5]上是增函数[-π/5,π/5]包含于[-π/(2w),π/(2w)]...