Introduction: A point $x$ such that $y'(x)=0$ is called a stationary point of the function $y(x)$.
Theorem: Assume $c$ is a stationary point of the function $y(x)$. It holds that:
Theorem: Assume $c$ is a stationary point of the function $y(x)$. It holds that:
- if $y'(x)< 0$ for each $x<c$ in the neighborhood of $c$ and $y'(x)> 0$ for each $x>c$ in the neighborhood of $c$, then $y(c)$ is a minimum
- if $y'(x)> 0$ for each $x< c$ in the neighborhood of $c$ and $y'(x)< 0$ for each $x>c$ in the neighborhood of $c$, then $y(c)$ is a maximum.