query: $f:\mathbb R \to \mathbb R$ is a differentiable function such that $f'(x)\le r<1 $ , does $f$ necessarily have a fixed point ?
positive_passages.docid: 150373
positive_passages.text: Number of Fixed Point(s) of a Differentiable Function
negative_passages.docid: 52632
negative_passages.text: $f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
negative_passages.docid: 93712
negative_passages.text: Let $f:(-1,1) \rightarrow \mathbb{R}$ be smooth on $(-1,1)$, $f(0) = 1$. Find $f(x)$.
negative_passages.docid: 37850
negative_passages.text: Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
negative_passages.docid: 139720
negative_passages.text: Are all continuous one one functions differentiable?
negative_passages.docid: 83707
negative_passages.text: Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it.
negative_passages.docid: 39057
negative_passages.text: Check the differentiablity of $\theta :\mathbb R^2 \setminus\{(0,0)\}\to \mathbb R$
negative_passages.docid: 124346
negative_passages.text: Where is $f(z)=\Re (z)$ differentiable?
negative_passages.docid: 107727
negative_passages.text: $m\{x\in [0,1]:f'(x)=0\}>0$
negative_passages.docid: 86472
negative_passages.text: $f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
negative_passages.docid: 11319
negative_passages.text: Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
negative_passages.docid: 100765
negative_passages.text: If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
negative_passages.docid: 85623
negative_passages.text: Proof of continuity implied by differentiability
negative_passages.docid: 19146
negative_passages.text: Showing that $f$ has exactly one fixed point
negative_passages.docid: 102143
negative_passages.text: $f:\mathbb R\rightarrow \mathbb R$ be a continuous function such that $\int_{0}^{\infty}f(x)dx$ exists.
negative_passages.docid: 154881
negative_passages.text: Question on differentiability of a continuous function
negative_passages.docid: 44144
negative_passages.text: If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?