query: Give an example of a continuous function $f$ from real to real which is not differentiable precisely at set of rationals
positive_passages.docid: 156839
positive_passages.text: Functions Which are non differentiable on a Given Set.
negative_passages.docid: 30036
negative_passages.text: Function in $H^1$, but not continuous
negative_passages.docid: 71487
negative_passages.text: Real Analysis: Continuity of a Composition Function
negative_passages.docid: 121848
negative_passages.text: If $f(x)=\begin {cases} x^a\sin (1/x) & x\not =0 \\ 0 & x =0 \end {cases}$ is continuous but not differentiable at $x=0$ find $a$
negative_passages.docid: 100436
negative_passages.text: Examples of nowhere continuous functions
negative_passages.docid: 3801
negative_passages.text: Functions that take rationals to rationals
negative_passages.docid: 11167
negative_passages.text: A counterexample of a differentiable function on an interval whose derivative is discontinuous
negative_passages.docid: 113450
negative_passages.text: Construction of a function which is not the pointwise limit of a sequence of continuous functions
negative_passages.docid: 38923
negative_passages.text: What can we say about differentiability of $f$ at $c$?
negative_passages.docid: 19916
negative_passages.text: $f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
negative_passages.docid: 30590
negative_passages.text: Are "most" continuous functions also differentiable?
negative_passages.docid: 143593
negative_passages.text: A sequence of differentiable functions that converge uniformly to a non differentiable function - is my example correct?
negative_passages.docid: 33488
negative_passages.text: A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
negative_passages.docid: 89257
negative_passages.text: Give an example of a function $f:\mathbb{R}^2 \mapsto \mathbb{R}^2$ such that
negative_passages.docid: 144426
negative_passages.text: Example of a function $f:\mathbb{R}^2\to\mathbb{R}$ not differentiable at $(0,0)$, but has a directional derivative at $(0,0)$ in all directions
negative_passages.docid: 113503
negative_passages.text: Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
negative_passages.docid: 53376
negative_passages.text: A continuous, nowhere differentiable but invertible function?