设函数f(x)=sinwx(w>0)在区间[-π/5,π/3]上是增函数,则w的取值范围是

设函数f(x)=sinwx(w>0)在区间[-π/5,π/3]上是增函数,则w的取值范围是

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/3]上是增函数
[-π/5,π/3]被包含于[-π/(2w),π/(2w)]
∴π/5≤π/(2w)且π/3≥π/(2w)
∴2/3≤w≤5/2