query: Is $F$ continuously differentiable at $x=0$?
positive_passages.docid: 147758
positive_passages.text: Differentiable but not continuously differentiable.
negative_passages.docid: 87743
negative_passages.text: Is a function whose derivative vanishes at rationals constant?
negative_passages.docid: 84785
negative_passages.text: Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
negative_passages.docid: 150833
negative_passages.text: Discontinuities of the derivative of a differentiable function on closed interval
negative_passages.docid: 10564
negative_passages.text: $f$ be a smooth function on real line , $f(0)=0$ , $f(x)>0, \forall x \ne 0$ and any $f^{(n)}(0)=0$ ; is $\sqrt f$ smooth?
negative_passages.docid: 27888
negative_passages.text: Why is $|x|$ not differentiable at $x=0$?
negative_passages.docid: 97735
negative_passages.text: Continuous functions are differentiable on a measurable set?
negative_passages.docid: 139720
negative_passages.text: Are all continuous one one functions differentiable?
negative_passages.docid: 6417
negative_passages.text: Can a function be differentiable at the end points of its (closed interval) domain?
negative_passages.docid: 49587
negative_passages.text: Does a differentiable everywhere function have a continuous derivative?
negative_passages.docid: 152877
negative_passages.text: Is a monotone differentiable function continuously differentiable?
negative_passages.docid: 96973
negative_passages.text: If $F(0,0)=0$ and $F(x,y)= \frac{xy}{x^2+y^2}$ for $(x,y)\neq (0,0)$ then $F$ is differentiable at $(0,0)$?
negative_passages.docid: 154881
negative_passages.text: Question on differentiability of a continuous function
negative_passages.docid: 135199
negative_passages.text: Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous
negative_passages.docid: 93528
negative_passages.text: Continuous versus differentiable
negative_passages.docid: 113975
negative_passages.text: Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
negative_passages.docid: 100765
negative_passages.text: If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?