若存在实常数\(k\)和\(b\),使得函数\({F}\left( x \right)\)和\({G}\left( x \right)\)对其公共定义域上的任意实数\(x\)都满足:\(F\left( x \right)\geqslant kx+b\)和\(G\left( x \right)\leqslant kx+b\)恒成立,则称此直线\(y=kx+b\)为\(F\left( x \right)\)和\(G\left( x \right)\)的“隔离直线”,已知函数\(f\left( x \right)={{x}^{2}}\left( x\in R \right)\),\(g\left( x \right)=\dfrac{1}{x}\left( x < 0 \right),h\left( x \right)=2e\ln x\),有下列命题:
\(①F\left( x \right)=f\left( x \right)-g\left( x \right)\)在\(x\in \left( -\dfrac{1}{\sqrt[3]{2}},0 \right)\)内单调递增;
\(②f\left( x \right)\)和\(g\left( x \right)\)之间存在“隔离直线”,且\({b}\)的最小值为\(-4\);
\(③f\left( x \right)\)和\(g\left( x \right)\)之间存在“隔离直线”,且\(k\)的取值范围是\((-4,0] \);
\(④f\left( x \right)\)和\(h\left(x\right) \)之间存在唯一的“隔离直线”\(y=2 \sqrt{e}x-e \).
其中真命题的个数有\((\) \()\)