query: Is there an open interval on which f is monotone? explain why?
positive_passages.docid: 157500
positive_passages.text: Are continuous functions monotonic for very small ranges?
negative_passages.docid: 125233
negative_passages.text: Why is an open interval not a compact set?
negative_passages.docid: 158230
negative_passages.text: prove that a non constant periodic, continuous function has a "smallest period"
negative_passages.docid: 149390
negative_passages.text: Fixed point of a Function (monotonically increasing)
negative_passages.docid: 153510
negative_passages.text: Questions about the existence of a function
negative_passages.docid: 78786
negative_passages.text: Why does an open interval NOT have measure zero?
negative_passages.docid: 50472
negative_passages.text: If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$
negative_passages.docid: 72006
negative_passages.text: Suppose $f(x)$ is linear i.e. $f(x + y) = f(x) +f(y) $ and monotone on $[-\infty, +\infty]$, then $f(x) = ax$, a real.
negative_passages.docid: 152877
negative_passages.text: Is a monotone differentiable function continuously differentiable?
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: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
negative_passages.docid: 24749
negative_passages.text: Monotone functions and Borel sets
negative_passages.docid: 39692
negative_passages.text: The length of an interval covered by an infinite family of open intervals
negative_passages.docid: 40576
negative_passages.text: Intermediate value property problem and continuous function
negative_passages.docid: 118400
negative_passages.text: Is there a monotonic function discontinuous over some dense set?
negative_passages.docid: 55268
negative_passages.text: Differentiable and Continuous functions on [0,1] with 'weird' conditions.
negative_passages.docid: 76396
negative_passages.text: Nowhere monotonic continuous function