A：$\exists x_0\in R,\forall x\in R$且$x\ne 0$，$f\left(x\right)\le f\left(x_0\right)$

B：$\exists x_0\in R,\forall x\in R$且$x\ne 0$，$f\left(x\right)\ge f\left(x_0\right)$

C：$\exists x_0\in R,\forall x\in \left(x_0,+\infty \right),f^{\text{'}}\left(x\right)<0$

D：$\exists x_0\in R,\forall x\in \left(x_0,+\infty \right),f^{\text{'}}\left(x\right)>0$