Let $U$ be an open set in $\mathbb{R}^n$ and $f : U \rightarrow \mathbb{R}^m$ be a differentiable function.
$a, b \in U$,
$L := \{a + t (b - a) \mid t \in [0, 1]\} \subset U$,
$|A| := \left(\sum_{i = 1}^m \sum_{j = 1}^n a_{i j}^2\right)^{\frac{1}{2}}$.
Does $\{|f'(x)| \mid x \in L\}$ have an upper bound?