Question

For $f$ continuous in $[0,1]$, differentiable in $(0,1)$ s.t. $f(0)=0$, prove $|f'(x_0)|\geq |f(x)|$ for some $x_0$ and all $x$ in $[0,1]$

score 65 · Answer 1 · 2018-05-30 21:26:34

65

Views

For $f$ continuous in $[0,1]$, differentiable in $(0,1)$ s.t. $f(0)=0$, prove $|f'(x_0)|\geq |f(x)|$ for some $x_0$ and all $x$ in $[0,1]$

Published on 30 May 2018 - 21:26

score 42 · Answer 2 · 2018-05-31 05:02:59

42

Views

Extend a continuous function $f$ to be a function mapping into $\mathbb{R} \cup \{+\infty\}$

Published on 31 May 2018 - 5:02

score 86 · Answer 3 · 2026-03-23 04:56:11

86

Views

How to prove that the following subgroup is normal?

Published on 23 Mar 2026 - 4:56

score 60 · Answer 4 · 2018-05-31 11:41:01

60

Views

Smooth bounded function equals average on a unit circumference -> it is constant?

Published on 31 May 2018 - 11:41

score 69 · Answer 5 · 2026-03-25 17:33:52

Let $f: \mathbb R\to \mathbb R$ be a continuous function. Which of the following are sufficient conditions for $f$ to have a fixed point in $[0, 1]$?

score 400 · Answer 6 · 2018-05-31 18:58:29

400

Views

Mistake in proof of $\overline{C_c(X)} = C_0(X)$..

Published on 31 May 2018 - 18:58

score 299 · Answer 7 · 2026-03-27 23:48:44

299

Views

Is this a proof that $\operatorname{Si}(x)$ is well-defined, continuous and bounded?

Published on 27 Mar 2026 - 23:48

score 68 · Answer 8 · 2018-06-01 06:09:55

68

Views

Finding $f(\sqrt 3 )$

Published on 01 Jun 2018 - 6:09

score 21 · Answer 9 · 2018-06-01 08:23:50

21

Views

A problem with Epsilon-Delta Continuity regarding a multivariable function

Published on 01 Jun 2018 - 8:23

score 252 · Answer 10 · 2026-03-25 12:15:19

252

Views

Continuity of inverse using epsilon delta

Published on 25 Mar 2026 - 12:15

score 55 · Answer 11 · 2026-03-26 04:50:44

55

Views

Example of strictly increasing discontinuous function with intermediate property on non compact set

Published on 26 Mar 2026 - 4:50

score 64 · Answer 12 · 2026-03-25 11:12:16

64

Views

Showing that $u$ is continuous in $\overline{\mathbb{D}}$

Published on 25 Mar 2026 - 11:12

score 1.1k · Answer 13 · 2026-03-25 06:05:24

1.1k

Views

Is there a way to phrase "continuous" in terms of "connected"?

Published on 25 Mar 2026 - 6:05

score 578 · Answer 14 · 2026-03-26 06:28:47

578

Views

The inverse of a continuous one-to-one function that is defined on a connected set is not always continuous

Published on 26 Mar 2026 - 6:28

score 1.8k · Answer 15 · 2018-06-02 17:34:46

1.8k

Views

Right continuous and monotone function must exist right derivative?

Published on 02 Jun 2018 - 17:34

List Question

For $f$ continuous in $[0,1]$, differentiable in $(0,1)$ s.t. $f(0)=0$, prove $|f'(x_0)|\geq |f(x)|$ for some $x_0$ and all $x$ in $[0,1]$

Extend a continuous function $f$ to be a function mapping into $\mathbb{R} \cup \{+\infty\}$

How to prove that the following subgroup is normal?

Smooth bounded function equals average on a unit circumference -> it is constant?

Let $f: \mathbb R\to \mathbb R$ be a continuous function. Which of the following are sufficient conditions for $f$ to have a fixed point in $[0, 1]$?

Mistake in proof of $\overline{C_c(X)} = C_0(X)$..

Is this a proof that $\operatorname{Si}(x)$ is well-defined, continuous and bounded?

Finding $f(\sqrt 3 )$

A problem with Epsilon-Delta Continuity regarding a multivariable function

Continuity of inverse using epsilon delta

Example of strictly increasing discontinuous function with intermediate property on non compact set

Showing that $u$ is continuous in $\overline{\mathbb{D}}$

Is there a way to phrase "continuous" in terms of "connected"?

The inverse of a continuous one-to-one function that is defined on a connected set is not always continuous

Right continuous and monotone function must exist right derivative?

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