已知$f(x)=2\sqrt{(\cos x+\frac{1}{2})^2+\sin x^2}-\sqrt{\cos x^2+(\sin x-\frac{1}{2})^2}$,若$m\ge f(x)$恒成立,求$m$的范围_______.
提示:
设 $A'(-\dfrac{1}{2},0),B(0,\dfrac{1}{2}),A(-2,0),P(x,y)$为单位圆上的点，
则$f(x)=2|PA'|-|PB|=|PA|-|PB|\le |AB|=\dfrac{\sqrt{17}}{2}$故$m\ge\dfrac{\sqrt{17}}{2}$