List questions from maxima-minima

Published on 10 Apr 2026 - 23:31

28

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Proving that, if $y_1\geq y_2$ at some interval $[x_0, x_1]$, there exists a point where $y_1'>y_2'$

Published on 22 Sep 2020 - 15:08

66

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Maxima and minima of trigonometric expressions

Published on 22 Sep 2020 - 16:28

69

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Minimum value of $f(x,y,z) = x^z + y^z - (xy)^{\frac{z}{4}}, x > 0, y > 0, z > 0$

Published on 01 Apr 2026 - 3:45

57

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Is $|\sum_{k=1}^{N}e^{2\pi i x_{k}}|$ bounded (with respect to other conditions)?

Published on 23 Sep 2020 - 11:48

610

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Find maximum of $|\sqrt{x^4-7x^2-4x+20}-\sqrt{x^4+9x^2+16}|$ without using calculus

Published on 23 Sep 2020 - 17:15

105

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$\min_{b \in \mathbb R}(| a_1−b |+ | a_2−b |+\dots+ | a_m−b |)$ .

Published on 24 Sep 2020 - 6:13

77

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Minimise $\sum \left\lvert x_j \right\rvert^2 + \sum \left\lvert y_j \right\rvert^2$ subject to the constraints $\sum x_j = 1$ and $\sum y_j = 0$.

Published on 24 Sep 2020 - 7:20

55

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Continuity of the minimizer of a parametrized function

Published on 11 Apr 2026 - 3:34

66

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A limit integral inequality

Published on 24 Sep 2020 - 13:01

163

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If $a^2x^4+b^2y^4=c^6$, then the maximum value of $xy$

Published on 01 Apr 2026 - 3:44

66

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Show $F(x,y)=f(1+x^2+y^2)$ has a local minimum at $(0,0)$

Published on 24 Sep 2020 - 18:08

64

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Can a function have its maximum value other than at the maxima given by calculus?

Published on 11 Apr 2026 - 16:19

45

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Solve the given word problem based on maximizing functions.

Published on 11 Apr 2026 - 18:23

97

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Maximum of $xy^4+x^4y$ given $x+y=1$

Published on 28 Sep 2020 - 13:56

List Question

Maximum sum of squares

Proving that, if $y_1\geq y_2$ at some interval $[x_0, x_1]$, there exists a point where $y_1'>y_2'$

Maxima and minima of trigonometric expressions

Minimum value of $f(x,y,z) = x^z + y^z - (xy)^{\frac{z}{4}}, x > 0, y > 0, z > 0$

Is $|\sum_{k=1}^{N}e^{2\pi i x_{k}}|$ bounded (with respect to other conditions)?

Find maximum of $|\sqrt{x^4-7x^2-4x+20}-\sqrt{x^4+9x^2+16}|$ without using calculus

$\min_{b \in \mathbb R}(| a_1−b |+ | a_2−b |+\dots+ | a_m−b |)$ .

Minimise $\sum \left\lvert x_j \right\rvert^2 + \sum \left\lvert y_j \right\rvert^2$ subject to the constraints $\sum x_j = 1$ and $\sum y_j = 0$.

Continuity of the minimizer of a parametrized function

A limit integral inequality

If $a^2x^4+b^2y^4=c^6$, then the maximum value of $xy$

Show $F(x,y)=f(1+x^2+y^2)$ has a local minimum at $(0,0)$

Can a function have its maximum value other than at the maxima given by calculus?

Solve the given word problem based on maximizing functions.

Maximum of $xy^4+x^4y$ given $x+y=1$

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