This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 3

2017 Mathematical Talent Reward Programme, MCQ: P 10
Tags: differentiable functions , limit , calculus , function
Let $f:\mathbb{R}\to \mathbb{R}$ be a differentiable function such that $\lim \limits_{x\to \infty}f'(x)=1$, then [list=1] [*] $f$ is increasing [*] $f$ is unbounded [*] $f'$ is bounded [*] All of these [/list]

2023 Romania National Olympiad, 1
Tags: real analysis , differentiable functions
Determine twice differentiable functions $f: \mathbb{R} \rightarrow \mathbb{R}$ which verify relation \[ \left( f'(x) \right)^2 + f''(x) \leq 0, \forall x \in \mathbb{R}. \]

2015 Mathematical Talent Reward Programme, MCQ: P 13
Tags: trigonometry , differentiable functions , calculus
Define $f(x)=\max \{\sin x, \cos x\} .$ Find at how many points in $(-2 \pi, 2 \pi), f(x)$ is not differentiable? [list=1] [*] 0 [*] 2 [*] 4 [*] $\infty$ [/list]