The subgradient has definition of:
$$ \partial f(x) = \{g;f(y) \ge f(x)+ g^T(y-x), \forall y \in dom(f) \} $$
My question is, when function f is convex function and differentiable, why it's the case that that $\nabla{f(x)}$ is the unique subgradient that exist at that point x?
If I understand right, problem can be transformed to, in the one dimensional case, why line of the slope of the gradient is the only line that passed (x, f(x)) and be below all other points in the function.
