# Tangent cone and maps between manifolds

Let $$f: \mathbb{R}^{l} \to \mathbb{R}^{k}$$ be continuously differentiable, and let $$S=f^{-1}(0)$$. Assume that, for some $$y \in S$$, $$f'(y)$$ has rank $$k$$. Show that $$T(y,S)=\text{ker} f'(x)$$, where $$T(y,S)$$ is the tangent cone of $$S$$ at $$y$$.