point d'inflexion tikz

%point d'inflexion
\begin{center}
\begin{tikzpicture}[x=1cm, y=.75cm]

\pgfmathsetmacro{\xmin}{-2}
\pgfmathsetmacro{\ymin}{-2}
\pgfmathsetmacro{\xmax}{6}
\pgfmathsetmacro{\ymax}{5}

%Axes
\draw[>={angle 60},thick,->,color=black] (\xmin,0) -- (\xmax,0) node[above] {$x$} node[below] {$\mathbb{R}$};
\draw[>={angle 60},thick,->,color=black] (0,\ymin) -- (0,\ymax) node[right] {$y$} node[left] {$\mathbb{R}$};

\clip (-2,-2) rectangle (6,5);
\draw[thick,shift={(2,0)},color=red] (0,0.05) -- (0,-0.05) node[below] {$\vphantom{(t)}a$};
\draw[color=black,smooth,samples=100,domain=-1:4.9,thick] plot (\x,{.25*pow(\x,3)-1.5*pow(\x,2)+(2)*(\x)+(2)}) node[below right] {$\mathscr{C}_f$};
\draw[color=red,thick]  (-1,5) -- node[pos=.95,left] {$T_a$} (5,-1);

\draw[fill,color=red] (2,2) circle (1pt);
\end{tikzpicture}
\end{center}