Question

How to maximize $\sum x_i\times x_j$ as $1\leq i,j\leq n$ with $i\neq j$ subject to $\sum x_i=1$?

score 635 · Answer 1 · 2020-11-07 11:18:43

635

Views

How to maximize $\sum x_i\times x_j$ as $1\leq i,j\leq n$ with $i\neq j$ subject to $\sum x_i=1$?

Published on 07 Nov 2020 - 11:18

score 35 · Answer 2 · 2020-11-07 14:10:09

35

Views

$x^2 - y^2=9$, $2y-x=3$, Find maximum value of $\dfrac{y}{x}$

Published on 07 Nov 2020 - 14:10

score 37 · Answer 3 · 2026-04-11 23:21:29

37

Views

Calculating maximum possible time of arrival difference

Published on 11 Apr 2026 - 23:21

score 100 · Answer 4 · 2020-11-09 05:52:17

100

Views

Minimum value of $(\sin x + \cos x)^3 + \frac{1}{\sin^2x\cos^2x}$

Published on 09 Nov 2020 - 5:52

score 37 · Answer 5 · 2026-04-10 08:29:28

37

Views

Finding local extrema with first derivative test

Published on 10 Apr 2026 - 8:29

score 85 · Answer 6 · 2020-11-10 03:31:51

85

Views

To find $h=\max_{a,b}(\min\{a, f(a,b)\}), a\geq 0, b\geq 0$

Published on 10 Nov 2020 - 3:31

score 85 · Answer 7 · 2026-04-03 07:11:51

85

Views

Logarithm inequality including square root:minimum of $\sqrt{\log_2^2a+1}+\sqrt{\log_2^2b+1}+\sqrt{\log_2^2c+1}$

Published on 03 Apr 2026 - 7:11

score 35 · Answer 8 · 2026-04-11 22:53:40

35

Views

Maxima of expression on given interval

Published on 11 Apr 2026 - 22:53

score 61 · Answer 9 · 2020-11-10 17:19:57

61

Views

Let $z$ be a complex number satisfying $|z|^4-16|z|^2-3(z^2+{\overline{z}}^2)+9=0$ ..

Published on 10 Nov 2020 - 17:19

score 54 · Answer 10 · 2020-11-11 12:37:22

54

Views

How small can $\max_{x \ge 0} e^x f'(x)$ be in terms of $\max_{x \ge 0} e^x f(x)$ if $f \ge 0$, $f(0) = 0$ and $\int_0^\infty f(x) dx = 1$

Published on 11 Nov 2020 - 12:37

score 100 · Answer 11 · 2026-04-12 02:54:08

100

Views

Are there any increasing or decreasing intervals of a quadratic equation with no real values of $x$?

Published on 12 Apr 2026 - 2:54

score 152 · Answer 12 · 2020-11-11 18:00:05

152

Views

$ \cos x\geq 1-\frac{x^2}{2} $

Published on 11 Nov 2020 - 18:00

score 200 · Answer 13 · 2026-04-10 20:40:55

200

Views

Maximum value at an endpoint

Published on 10 Apr 2026 - 20:40

score 160 · Answer 14 · 2026-04-09 23:23:08

160

Views

Optimizing a function with no local maximum?

Published on 09 Apr 2026 - 23:23

score 71 · Answer 15 · 2026-04-12 08:41:32

71

Views

Existence Nash Equilibria for zero-sum games

Published on 12 Apr 2026 - 8:41

List Question

How to maximize $\sum x_i\times x_j$ as $1\leq i,j\leq n$ with $i\neq j$ subject to $\sum x_i=1$?

$x^2 - y^2=9$, $2y-x=3$, Find maximum value of $\dfrac{y}{x}$

Calculating maximum possible time of arrival difference

Minimum value of $(\sin x + \cos x)^3 + \frac{1}{\sin^2x\cos^2x}$

Finding local extrema with first derivative test

To find $h=\max_{a,b}(\min\{a, f(a,b)\}), a\geq 0, b\geq 0$

Logarithm inequality including square root:minimum of $\sqrt{\log_2^2a+1}+\sqrt{\log_2^2b+1}+\sqrt{\log_2^2c+1}$

Maxima of expression on given interval

Let $z$ be a complex number satisfying $|z|^4-16|z|^2-3(z^2+{\overline{z}}^2)+9=0$ ..

How small can $\max_{x \ge 0} e^x f'(x)$ be in terms of $\max_{x \ge 0} e^x f(x)$ if $f \ge 0$, $f(0) = 0$ and $\int_0^\infty f(x) dx = 1$

Are there any increasing or decreasing intervals of a quadratic equation with no real values of $x$?

$ \cos x\geq 1-\frac{x^2}{2} $

Maximum value at an endpoint

Optimizing a function with no local maximum?

Existence Nash Equilibria for zero-sum games

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