query: $f>0$, $f'\geq 0$ but not continuous.
positive_passages.docid: 152877
positive_passages.text: Is a monotone differentiable function continuously differentiable?
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: 111485
negative_passages.text: Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
negative_passages.docid: 18082
negative_passages.text: A continuous function that attains neither its minimum nor its maximum at any open interval is monotone
negative_passages.docid: 20273
negative_passages.text: Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
negative_passages.docid: 151573
negative_passages.text: Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
negative_passages.docid: 129551
negative_passages.text: Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
negative_passages.docid: 76607
negative_passages.text: Show that exists a continuous function in $E$ that is not bounded
negative_passages.docid: 57026
negative_passages.text: $f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
negative_passages.docid: 145368
negative_passages.text: How to show $f:Y\to X^{+}$ is continuous?
negative_passages.docid: 33523
negative_passages.text: If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
negative_passages.docid: 62817
negative_passages.text: Functions which are Continuous, but not Bicontinuous
negative_passages.docid: 149095
negative_passages.text: $f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
negative_passages.docid: 127538
negative_passages.text: Show $f(x)=x\ln x$ is not uniformly continuous
negative_passages.docid: 76396
negative_passages.text: Nowhere monotonic continuous function
negative_passages.docid: 136714
negative_passages.text: Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
negative_passages.docid: 147758
negative_passages.text: Differentiable but not continuously differentiable.