Question

Proving that $f(x,y)=(2x^2-y)(y-x^2)$ has positive and negative function values in every neighborhood around $(0,0)$

score 60 · Answer 1 · 2026-04-12 18:57:17

60

Views

Proving that $f(x,y)=(2x^2-y)(y-x^2)$ has positive and negative function values in every neighborhood around $(0,0)$

Published on 12 Apr 2026 - 18:57

score 559 · Answer 2 · 2026-04-13 19:27:57

559

Views

Computing local and global minima on Wolfram Alpha

Published on 13 Apr 2026 - 19:27

score 151 · Answer 3 · 2026-04-12 00:57:13

151

Views

Calculate maximum and minimum when second partial derivative test fail

Published on 12 Apr 2026 - 0:57

score 108 · Answer 4 · 2026-04-15 18:07:38

108

Views

Finding the range of $f(x)=\log_2\left(4^{x^2}+4^{(x-1)^2}\right)$

Published on 15 Apr 2026 - 18:07

score 49 · Answer 5 · 2026-04-13 22:39:25

49

Views

What is the relation between the sentences "$f$ achieves its minimum" and "$f$ is bounded from below"?

Published on 13 Apr 2026 - 22:39

score 202 · Answer 6 · 2026-04-13 09:03:00

202

Views

Existence of a minimer when dealing with a coercive functional: how to prove it?

Published on 13 Apr 2026 - 9:03

score 175 · Answer 7 · 2026-04-13 10:42:19

175

Views

What does it mean that $f$ achieves its minimum?

Published on 13 Apr 2026 - 10:42

score 666 · Answer 8 · 2026-04-12 03:01:08

666

Views

Finding minimum $ x $ value that minimizes a function.

Published on 12 Apr 2026 - 3:01

score 393 · Answer 9 · 2026-04-11 10:55:23

393

Views

Finding the maximum/minimum of a modulo function

Published on 11 Apr 2026 - 10:55

score 227 · Answer 10 · 2026-04-15 17:20:36

227

Views

For an acute angled triangle $ABC,$ if $p=\frac{\sqrt3+\sin A+\sin B+\sin C}{2\sin A\sin B\sin C}$, find the range of $p$

Published on 15 Apr 2026 - 17:20

score 88 · Answer 11 · 2026-04-10 18:52:21

88

Views

What are the properties of a function for which the function attains its maxima or minima when all the variables of the function are equal?

Published on 10 Apr 2026 - 18:52

score 428 · Answer 12 · 2026-04-17 02:08:11

428

Views

(Typo?): Find the minimum value of the function $x^3+y^3-3xy$.

Published on 17 Apr 2026 - 2:08

score 108 · Answer 13 · 2026-04-17 02:42:30

108

Views

Determine the minimum value of: $P=\frac{\sqrt{x^2+xy+y^2}}{(x+y)^2+1}+\frac{\sqrt{y^2+yz+z^2}}{(y+z)^2+1}+\frac{\sqrt{z^2+zx+x^2}}{(z+x)^2+1}.$

Published on 17 Apr 2026 - 2:42

score 24 · Answer 14 · 2026-04-10 20:39:15

24

Views

can $u$ attain a local maxima at $x_0$?

Published on 10 Apr 2026 - 20:39

score 43 · Answer 15 · 2026-04-12 03:04:46

43

Views

First Derivative at a saddle point

Published on 12 Apr 2026 - 3:04

List Question

Proving that $f(x,y)=(2x^2-y)(y-x^2)$ has positive and negative function values in every neighborhood around $(0,0)$

Computing local and global minima on Wolfram Alpha

Calculate maximum and minimum when second partial derivative test fail

Finding the range of $f(x)=\log_2\left(4^{x^2}+4^{(x-1)^2}\right)$

What is the relation between the sentences "$f$ achieves its minimum" and "$f$ is bounded from below"?

Existence of a minimer when dealing with a coercive functional: how to prove it?

What does it mean that $f$ achieves its minimum?

Finding minimum $ x $ value that minimizes a function.

Finding the maximum/minimum of a modulo function

For an acute angled triangle $ABC,$ if $p=\frac{\sqrt3+\sin A+\sin B+\sin C}{2\sin A\sin B\sin C}$, find the range of $p$

What are the properties of a function for which the function attains its maxima or minima when all the variables of the function are equal?

(Typo?): Find the minimum value of the function $x^3+y^3-3xy$.

Determine the minimum value of: $P=\frac{\sqrt{x^2+xy+y^2}}{(x+y)^2+1}+\frac{\sqrt{y^2+yz+z^2}}{(y+z)^2+1}+\frac{\sqrt{z^2+zx+x^2}}{(z+x)^2+1}.$

can $u$ attain a local maxima at $x_0$?

First Derivative at a saddle point

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