Let $[a, b] \subseteq \mathbb{R}$ be a
D544: Closed real interval such that
| (i) |
\begin{equation}
a < b
\end{equation}
|
| (ii) |
$f : [a, b] \to \mathbb{R}$ is a D5231: Standard-continuous real function on $[a, b]$
|
| (iii) |
$f$ is a D5614: Differentiable real function at $x_0 \in (a, b)$
|
| (iv) |
One of the following statements is true
| (a) |
\begin{equation}
\exists \, r > 0 :
\forall \, x \in (x_0 - r, x_0 + r) :
f(x_0) \geq f(x)
\end{equation}
|
| (b) |
\begin{equation}
\exists \, r > 0 :
\forall \, x \in (x_0 - r, x_0 + r) :
f(x_0) \leq f(x)
\end{equation}
|
|
Then
\begin{equation}
f'(x_0) = 0
\end{equation}
