A function is Carathéodory differentiable at if there exists a function which is continuous at such that
Every function which is Carathéodory differentiable is also Fréchet differentiable.
A function is Carathéodory differentiable at if there exists a function which is continuous at such that
Every function which is Carathéodory differentiable is also Fréchet differentiable.
Weisstein, Eric W. "Carathéodory Derivative." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CaratheodoryDerivative.html