Suppose $y=f(x)$ is a continuous and twice differentiable function for all real numbers $x.$

Select all the correct statements below:

$($A$)$ If $f^{\text{'}}(c)=0,$ for some real number $c,$ then $f(x)$ must have a relative maximum at $x=c.$

If $f(x)$ is a rational function, then $f(x)$ may have horizontal and $/$ or vertical asymptotes.

If $f^{\text{'}}(c)=0,$ for some real number $c,$ then $f(x)$ must have a relative minimum at $x=c.$

If $f^{\text{'}\text{'}}(c)=0,$ for some real number $c,$ then $f(x)$ must have a point of inflection at $x=c.$

If $f(x)$ is a polynomial, then $f(x)$ does not have any horizontal or vertical asymptotes.

If $f(x)$ is not defined at $x=c$ then $c$ cannot be a point of inflection of $f(x).$

$($G$)$ If $f(x)$ is differentiable at $x=c,f^{\text{'}}(c)=0,$ and $f^{\text{'}\text{'}}(c)>0,$ then $f(x)$ has a relative minimum at $x=c.$

$($H$)$ If $f(x)$ is differentiable at $x=c,f^{\text{'}}(c)=0,$ and then $f(x)$ has a relative minimum at $x=c.$

If $f(x)$ is differentiable at $x=c,f^{\text{'}}(c)=0,$ and $f^{\text{'}\text{'}}(c)>0,$ then $f(x)$ has a relative maximum at $x=c.$

If $f^{\text{'}}(c)=0,$ for some real number $c,$ then $f(x)$ must have a point of inflection at $x=c.$

If $f(x)$ is differentiable at $x=c,f^{\text{'}}(c)=0,$ and then $f(x)$ has a relative maximum at $x=c.$