A function $f\left(x\right)$ has the following properties:

$f^{\prime }\left(x\right)>0$ and $f^{\prime }$${}^{\prime }\left(x\right)>0$, for $x>4$

Which of the following is a possible graph of $f\left(x\right)$?

Graph the function $f\left(x\right)=6-6x^{\frac{2}{3}}+x^{\frac{8}{3}}$. The first and second derivative are given.

$f^{\prime }\left(x\right)=-\frac{4}{x^{\frac{1}{3}}}+\frac{8}{3}{x}^{\frac{5}{3}}$

$f^{\prime \prime }\left(x\right)=\frac{4}{3x^{\frac{4}{3}}}+\frac{40}{9}{x}^{\frac{2}{3}}$

Graph the given classical curve using analytical methods.

$y^2=x^3-2x+3$ ; $\frac{dy}{dx}=\frac{3x^2-2}{2y}$