List questions from maxima-minima

Published on 24 Jun 2014 - 12:59

374

Views

Find maximum of $\sum\limits_{k=1}^n \sin^2{\theta_{k}}$ for $\theta_k \ge 0, \forall k$ with $\sum\limits_{k=1}^n \theta_k = \pi$

Published on 25 Jun 2014 - 16:22

121.2k

Views

maximum area of a rectangle inscribed in a semi - circle with radius r.

Published on 30 Mar 2026 - 10:39

96

Views

Minimum of $x^2+y^2+z^2$ subject to $ax+by+cz=1$

Published on 26 Mar 2026 - 17:34

69

Views

Local min/max of $y =(4+x)/(x^2-5)$

Published on 09 Oct 2014 - 23:18

7.8k

Views

Prove that there are infinitely many critical points and they are all local (and absolute) minima on $x^2+4y^2-4xy+2$

Published on 25 Mar 2026 - 4:43

192

Views

a two-variable cyclic power inequality $x^y+y^x>1$ intractable by standard calculus techniques

Published on 06 Nov 2014 - 17:41

2k

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Boundary solution to a max-min problem

Published on 08 Nov 2014 - 5:36

318

Views

local maxima of weierstrass function

Published on 11 Dec 2014 - 5:20

4.7k

Views

Greatest value of $f(x)= (x+1)^{1/3}-(x-1)^{1/3}$ on $(0,1)$

Published on 25 Mar 2026 - 11:21

187

Views

Find maximum and minimum of : $\Omega=\sin x\sin y\sin z$

Published on 26 Mar 2026 - 7:02

48

Views

Maxima and Minima, Critical value

Published on 07 Oct 2019 - 13:53

150

Views

Is this an n-th root of unity (on the regular polygon)?

Published on 26 Mar 2026 - 8:04

49

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local/global extremum

Published on 07 Oct 2019 - 16:50

56

Views

Maximum value of a cyclic sum

Published on 08 Oct 2019 - 3:42

List Question

A question about the boundedness theorem

Find maximum of $\sum\limits_{k=1}^n \sin^2{\theta_{k}}$ for $\theta_k \ge 0, \forall k$ with $\sum\limits_{k=1}^n \theta_k = \pi$

maximum area of a rectangle inscribed in a semi - circle with radius r.

Minimum of $x^2+y^2+z^2$ subject to $ax+by+cz=1$

Local min/max of $y =(4+x)/(x^2-5)$

Prove that there are infinitely many critical points and they are all local (and absolute) minima on $x^2+4y^2-4xy+2$

a two-variable cyclic power inequality $x^y+y^x>1$ intractable by standard calculus techniques

Boundary solution to a max-min problem

local maxima of weierstrass function

Greatest value of $f(x)= (x+1)^{1/3}-(x-1)^{1/3}$ on $(0,1)$

Find maximum and minimum of : $\Omega=\sin x\sin y\sin z$

Maxima and Minima, Critical value

Is this an n-th root of unity (on the regular polygon)?

local/global extremum

Maximum value of a cyclic sum

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