Inflexion Point

Tags

math

A stationary point where the gradient changes sign.

Stationary points don't always have to change the sign of the gradient, the gradient can simply drop to 0 momentarily and then continue increasing in the same direction it was going on before the stationary point (as shown in fig:inflexion-point-demo the gradient is increasing from -5 to 0 where it drops to 0, and then it's increasing from 1 to 5).

\begin{figure}
  \centering
  \begin{tikzpicture}
    \begin{axis}[axis lines=center, xmin=-5, xmax=5, ymin=-5, ymax=5, domain=-5:5, grid=both]
      \addplot[color=green]{x^3};,
      \addplot[only marks] coordinates {(0, 0)};,
    \end{axis}
  \end{tikzpicture}
  \qquad
  \caption{A graph with a single inflexion point.}
  \label{fig:inflexion-point-demo}
\end{figure}