Question

score 126 · Answer 1 · 2026-03-29 23:38:07

126

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Useful identity, $|ac - bd| \leq \max(a,b) | c-d| + \max(c,d)|a-b|$, how to prove?

Published on 29 Mar 2026 - 23:38

score 115 · Answer 2 · 2020-02-12 12:39:11

115

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Please show me how to approach and solve the problem: Find the minimum value of $ f(x)=x^{2}-4x+3+3\cos(\frac{\pi x}{4})$

Published on 12 Feb 2020 - 12:39

score 212 · Answer 3 · 2026-03-28 16:44:17

212

Views

Cusp form for $\text{SL}_2(\mathbb{Z})$ attaining a maximum on $\mathcal{D}=\{z\in\mathbb{H}\colon|\text{Re}(z)|\leq\frac12,\|z\|\geq 1\}$

Published on 28 Mar 2026 - 16:44

score 1.5k · Answer 4 · 2020-02-13 14:55:56

1.5k

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Can we say that $x=0$ is a minimum of the function $f(x)=|x|$?

Published on 13 Feb 2020 - 14:55

score 214 · Answer 5 · 2026-03-28 01:48:44

214

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If $h(x) = \dfrac{f(x)}{g(x)}$, then find the local minimum value of $h(x)$

Published on 28 Mar 2026 - 1:48

score 120 · Answer 6 · 2020-02-14 20:04:50

120

Views

Optimization of a trigonometric function on the unit circle

Published on 14 Feb 2020 - 20:04

score 380 · Answer 7 · 2026-02-23 12:58:14

380

Views

Find the minimum number of zeros of $g(x)=(f'(x))^2+f(x)f''(x)$in the interval $[a, e]$ for the following given information.

Published on 23 Feb 2026 - 12:58

score 113 · Answer 8 · 2020-02-14 23:02:11

113

Views

Find out the local maxima/minima of $\sin x$ where $x\in\left[\dfrac{\pi}{2},\dfrac{3\pi}{2}\right]$

Published on 14 Feb 2020 - 23:02

score 173 · Answer 9 · 2020-02-14 23:18:24

173

Views

Find out the local maxima/minima of $x^3$ in $[0,1]$?

Published on 14 Feb 2020 - 23:18

score 350 · Answer 10 · 2026-03-27 19:32:04

350

Views

Wien's Displacement Law and the Planck Function

Published on 27 Mar 2026 - 19:32

score 275 · Answer 11 · 2026-03-30 16:48:37

275

Views

Maximum value of $|z^{-1}-p(z)|$ for any polynomial $p(z)$

Published on 30 Mar 2026 - 16:48

score 93 · Answer 12 · 2020-02-16 22:58:49

93

Views

Maximize $\cos(2x) - e^{3x}$

Published on 16 Feb 2020 - 22:58

score 25 · Answer 13 · 2026-03-31 12:51:11

25

Views

Does $g$ have a minimum on $X$?

Published on 31 Mar 2026 - 12:51

score 1.1k · Answer 14 · 2026-03-29 08:16:08

1.1k

Views

Find the shortest distance from the origin to the surface of $x=yz+10$

Published on 29 Mar 2026 - 8:16

score 130 · Answer 15 · 2020-02-20 11:13:59

Is the answer sheet wrong? Maximum and minimum value of this $2\sin^3x + \frac 34 \sin 2x + \frac 92 \cos 2x - 9\cos x - \frac 32 x + 6 $

List Question

Useful identity, $|ac - bd| \leq \max(a,b) | c-d| + \max(c,d)|a-b|$, how to prove?

Please show me how to approach and solve the problem: Find the minimum value of $ f(x)=x^{2}-4x+3+3\cos(\frac{\pi x}{4})$

Cusp form for $\text{SL}_2(\mathbb{Z})$ attaining a maximum on $\mathcal{D}=\{z\in\mathbb{H}\colon|\text{Re}(z)|\leq\frac12,\|z\|\geq 1\}$

Can we say that $x=0$ is a minimum of the function $f(x)=|x|$?

If $h(x) = \dfrac{f(x)}{g(x)}$, then find the local minimum value of $h(x)$

Optimization of a trigonometric function on the unit circle

Find the minimum number of zeros of $g(x)=(f'(x))^2+f(x)f''(x)$in the interval $[a, e]$ for the following given information.

Find out the local maxima/minima of $\sin x$ where $x\in\left[\dfrac{\pi}{2},\dfrac{3\pi}{2}\right]$

Find out the local maxima/minima of $x^3$ in $[0,1]$?

Wien's Displacement Law and the Planck Function

Maximum value of $|z^{-1}-p(z)|$ for any polynomial $p(z)$

Maximize $\cos(2x) - e^{3x}$

Does $g$ have a minimum on $X$?

Find the shortest distance from the origin to the surface of $x=yz+10$

Is the answer sheet wrong? Maximum and minimum value of this $2\sin^3x + \frac 34 \sin 2x + \frac 92 \cos 2x - 9\cos x - \frac 32 x + 6 $

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