query: Additive function differentiable at 0
positive_passages.docid: 14578
positive_passages.text: Proving that an additive function $f$ is continuous if it is continuous at a single point
negative_passages.docid: 61486
negative_passages.text: Show that $f$ is not differentiable at $(0,0)$ - $\frac{x_1^2x_2}{x_1^2+x_2^2}$
negative_passages.docid: 12556
negative_passages.text: A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
negative_passages.docid: 95340
negative_passages.text: Locally bounded additive function is linear
negative_passages.docid: 73073
negative_passages.text: Differentiating $y=x^{2}$
negative_passages.docid: 84385
negative_passages.text: Implicit differentiation
negative_passages.docid: 130180
negative_passages.text: Smooth function with all derivatives zero
negative_passages.docid: 80547
negative_passages.text: If $0$ is the zero-object $ \Longrightarrow F(0) $ is the zero object when $F$ additive
negative_passages.docid: 137815
negative_passages.text: Additive but not $\sigma$-additive function
negative_passages.docid: 88311
negative_passages.text: Linear functional f(v)=0 imply v=0
negative_passages.docid: 111470
negative_passages.text: Proof of differentiability of $f(x)$
negative_passages.docid: 46923
negative_passages.text: Differentiable Sequences
negative_passages.docid: 144323
negative_passages.text: Differentiation of a function
negative_passages.docid: 28898
negative_passages.text: Is there a function $f: \mathbb R \to \mathbb R$ that has only one point differentiable?
negative_passages.docid: 72702
negative_passages.text: Estimate on the derivative at fixed point
negative_passages.docid: 37303
negative_passages.text: Differential of a smooth function
negative_passages.docid: 150005
negative_passages.text: Existence of points in a differentiable function