List questions from maxima-minima

78

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For any positive real numbers $a,b,c$, show that $\min\{(b-c)^2,(c-a)^2,(a-b)^2)\} \leq \frac{a^2+b^2+c^2}{5}$

Published on 25 Mar 2026 - 22:05

81

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Questions involving $f(x)=\begin{cases}x+1;&0\le x\le1\\2x^2-6x+6,&1\lt x\le2\end{cases}$ and $g(t)=\int_{t-1}^tf(x)dx$ for $t\in[1,2]$

Published on 17 Apr 2026 - 14:42

219

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Why the method of Lagrange multipliers fails in this case?

Published on 15 Apr 2026 - 7:30

37

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Minimizing an integral to find optimum Covid testing times

Published on 11 Apr 2026 - 8:57

57

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Why do we consider the lower bound in this Inequality?

Published on 16 Apr 2026 - 13:31

45

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Solution to minimization problem when parameter goes to infinity

Published on 09 Apr 2026 - 23:47

381

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Tight upper bound for the binary entropy function

Published on 15 Apr 2026 - 1:00

275

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Find the minimum value of: $\dfrac{a}{b+3a}+\dfrac{b}{c+3b}+\dfrac{c}{a+3c}$

Published on 15 Apr 2026 - 8:26

174

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How do you approach when completing the square?

Published on 11 Apr 2026 - 17:12

98

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Optimization of $g(x, y) = x^2 + (y + 24)^2$

Published on 16 Apr 2026 - 9:44

245

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Given the triangle ABC. Let BC = a, AC = b, AB = c. Find the minimum value of the following expression

Published on 25 Mar 2026 - 19:11

174

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Range minimization problems

Published on 11 Apr 2026 - 3:57

137

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Finding maximum/minimum using Lagrange multiplier

Published on 26 Mar 2026 - 1:09

166

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Maximum value of $2\sqrt 6ab+8bc$ when $a^2+b^2+c^2=1$.

Published on 17 Apr 2026 - 7:32

218

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Sum of two max operators

Published on 11 Apr 2026 - 3:18

List Question

For any positive real numbers $a,b,c$, show that $\min\{(b-c)^2,(c-a)^2,(a-b)^2)\} \leq \frac{a^2+b^2+c^2}{5}$

Questions involving $f(x)=\begin{cases}x+1;&0\le x\le1\\2x^2-6x+6,&1\lt x\le2\end{cases}$ and $g(t)=\int_{t-1}^tf(x)dx$ for $t\in[1,2]$

Why the method of Lagrange multipliers fails in this case?

Minimizing an integral to find optimum Covid testing times

Why do we consider the lower bound in this Inequality?

Solution to minimization problem when parameter goes to infinity

Tight upper bound for the binary entropy function

Find the minimum value of: $\dfrac{a}{b+3a}+\dfrac{b}{c+3b}+\dfrac{c}{a+3c}$

How do you approach when completing the square?

Optimization of $g(x, y) = x^2 + (y + 24)^2$

Given the triangle ABC. Let BC = a, AC = b, AB = c. Find the minimum value of the following expression

Range minimization problems

Finding maximum/minimum using Lagrange multiplier

Maximum value of $2\sqrt 6ab+8bc$ when $a^2+b^2+c^2=1$.

Sum of two max operators

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