Question

If $f$ is continuous, $f'(c)=0$ and $f''(c)<0$, then $f(x)<f(c)$ for all $x$ in an interval around $c$?

score 581 · Answer 1 · 2026-04-16 07:24:35

581

Views

If $f$ is continuous, $f'(c)=0$ and $f''(c)<0$, then $f(x)<f(c)$ for all $x$ in an interval around $c$?

Published on 16 Apr 2026 - 7:24

score 68 · Answer 2 · 2026-04-15 07:18:04

68

Views

Example of a function $f:\mathbb{R}^2\rightarrow\mathbb{R}$ such that $\partial_{u}f \neq \nabla f.\vec{u}$

Published on 15 Apr 2026 - 7:18

score 255 · Answer 3 · 2026-05-10 17:15:38

255

Views

Prove that $\frac{\sin(x)}{1+|x|}$ is not Lebesgue integrable

Published on 10 May 2026 - 17:15

score 76 · Answer 4 · 2026-04-11 08:51:03

76

Views

Strange asymptotic assertion in a proof

Published on 11 Apr 2026 - 8:51

score 58 · Answer 5 · 2026-04-24 02:24:58

58

Views

Prove $s\in L^1 and \int f = \int s$

Published on 24 Apr 2026 - 2:24

score 370 · Answer 6 · 2026-04-16 08:00:18

370

Views

Set of positive real numbers with finite non zero limit point can be arranged in sequence $(a_n)$ with $(a_n^{1/n})_n$ convergent

Published on 16 Apr 2026 - 8:00

score 61 · Answer 7 · 2026-04-14 16:51:00

example of two disjoint subsets $A$ and $B$ of $\Bbb R$ so that $A \cup B$ and $A$ are both open in $\Bbb R$ but $B$ is not open in $\Bbb R$

score 291 · Answer 8 · 2026-05-10 13:50:36

291

Views

Proof of Equivalent Definitions of Wedge Product

Published on 10 May 2026 - 13:50

score 45 · Answer 9 · 2026-04-17 12:43:39

45

Views

Why doesn't this converge uniformly?

Published on 17 Apr 2026 - 12:43

score 87 · Answer 10 · 2026-04-11 02:53:01

87

Views

Showing that $f(x)$ is well-defined and continuous on $\mathbb{R} \setminus \mathbb{Z}$.

Published on 11 Apr 2026 - 2:53

score 936 · Answer 11 · 2026-05-05 00:29:00

936

Views

Link between $p-variation$ and $Holder$ norm

Published on 05 May 2026 - 0:29

score 57 · Answer 12 · 2026-04-16 00:06:52

57

Views

show that function $f:\mathbb{R \to\mathbb{R}}$ defined by $f(x)=|x|^{p}$ for $p\geq1$ is a convex function.

Published on 16 Apr 2026 - 0:06

score 78 · Answer 13 · 2026-04-16 22:12:48

78

Views

Why is $W^{1,p}(\Omega;S)$ weakly closed in $W^{1,p}(\Omega;\mathbb R^N)$ for a compact set $S$?

Published on 16 Apr 2026 - 22:12

score 67 · Answer 14 · 2026-04-15 17:37:52

67

Views

discontinuity of $f(x) = \left \{ x \right \}* \left \{ -x \right \}$

Published on 15 Apr 2026 - 17:37

score 104 · Answer 15 · 2026-04-14 02:47:45

104

Views

Continuous, increasing function twice differentiable at a point must be once continuously differentiable in a neighbourhood.

Published on 14 Apr 2026 - 2:47

List Question

If $f$ is continuous, $f'(c)=0$ and $f''(c)<0$, then $f(x)<f(c)$ for all $x$ in an interval around $c$?

Example of a function $f:\mathbb{R}^2\rightarrow\mathbb{R}$ such that $\partial_{u}f \neq \nabla f.\vec{u}$

Prove that $\frac{\sin(x)}{1+|x|}$ is not Lebesgue integrable

Strange asymptotic assertion in a proof

Prove $s\in L^1 and \int f = \int s$

Set of positive real numbers with finite non zero limit point can be arranged in sequence $(a_n)$ with $(a_n^{1/n})_n$ convergent

example of two disjoint subsets $A$ and $B$ of $\Bbb R$ so that $A \cup B$ and $A$ are both open in $\Bbb R$ but $B$ is not open in $\Bbb R$

Proof of Equivalent Definitions of Wedge Product

Why doesn't this converge uniformly?

Showing that $f(x)$ is well-defined and continuous on $\mathbb{R} \setminus \mathbb{Z}$.

Link between $p-variation$ and $Holder$ norm

show that function $f:\mathbb{R \to\mathbb{R}}$ defined by $f(x)=|x|^{p}$ for $p\geq1$ is a convex function.

Why is $W^{1,p}(\Omega;S)$ weakly closed in $W^{1,p}(\Omega;\mathbb R^N)$ for a compact set $S$?

discontinuity of $f(x) = \left \{ x \right \}* \left \{ -x \right \}$

Continuous, increasing function twice differentiable at a point must be once continuously differentiable in a neighbourhood.

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