Second-order condition extremum

Introduction: The Second-order derivative can be used to determine whether a Stationary point is a minimum or a maximum.

Theorem: If $c$ is a stationary point of the function $y(x)$, then it holds that:

• if $y''(c)> 0$, then $y(c)$ is a minimum;
• if $y''(c)< 0$, then $y(c)$ is a maximum.

Remark: If $y''(c)=0$ the stationary point $c$ can be a minimum location, a maximum location or a saddle point.