Question

for any $e$ prove that the difference between $f(x)$ and $f(x+e)$ is the same as the directional derivative of $f(x+te)$ in the direction of $e$

score 83 · Answer 1 · 2026-04-15 13:46:28

83

Views

for any $e$ prove that the difference between $f(x)$ and $f(x+e)$ is the same as the directional derivative of $f(x+te)$ in the direction of $e$

Published on 15 Apr 2026 - 13:46

score 231 · Answer 2 · 2026-04-17 14:47:12

231

Views

Show that $\left|\int_a^b f(x) dx\right|\leqslant \frac{M}{12}(b-a)^3$?

Published on 17 Apr 2026 - 14:47

score 802 · Answer 3 · 2026-04-12 08:38:04

802

Views

What is chain rule for second order derivative of a composite function?

Published on 12 Apr 2026 - 8:38

score 1k · Answer 4 · 2026-04-16 15:05:24

1k

Views

Find the radius of a cylinder of given volume V if its surface area is a minimum.

Published on 16 Apr 2026 - 15:05

score 108 · Answer 5 · 2026-04-16 15:00:35

108

Views

Maximizing $f(x,y,z)$ over $\mathcal T=\left\{(x,y,z)\, |\, 0\leq y\leq x-1\, , \, x\in[1,2]\, , \, z\in\mathbb R \right\}$

Published on 16 Apr 2026 - 15:00

score 40 · Answer 6 · 2026-04-28 19:24:49

40

Views

Prove that a function has a root in interval, when you know, by Rolle, there is a root of the derivative, but you don't know it.

Published on 28 Apr 2026 - 19:24

score 243 · Answer 7 · 2026-04-14 19:22:13

243

Views

Prob. 7, Sec. 6.1, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: A necessary and sufficient condition for the existence of $\big(|f|\big)^\prime$

Published on 14 Apr 2026 - 19:22

score 44 · Answer 8 · 2026-04-15 18:52:19

44

Views

Find functions $f:\mathbb{R}^n\to\mathbb{R}, n\ge 2$ such that $\nabla f(x)= 0$ and $x$ is local min but not global, and $x$ is saddle point

Published on 15 Apr 2026 - 18:52

score 469 · Answer 9 · 2026-04-12 15:48:46

469

Views

How to reduce this to have only one x ...

Published on 12 Apr 2026 - 15:48

score 444 · Answer 10 · 2026-04-15 02:24:57

444

Views

Prob. 17, Sec. 6.1, in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: Straddle Lemma

Published on 15 Apr 2026 - 2:24

score 226 · Answer 11 · 2026-04-15 04:50:21

226

Views

Gradient of the maximum of smooth functions

Published on 15 Apr 2026 - 4:50

score 81 · Answer 12 · 2026-04-12 13:19:52

81

Views

Interesting Successive differentiation

Published on 12 Apr 2026 - 13:19

score 56 · Answer 13 · 2026-04-10 21:20:35

56

Views

Problem with Intuitive meaning of derivative

Published on 10 Apr 2026 - 21:20

score 414 · Answer 14 · 2026-04-15 18:25:56

414

Views

Second derivative finite difference of a convolution of two functions.

Published on 15 Apr 2026 - 18:25

score 741 · Answer 15 · 2026-04-29 06:48:06

741

Views

How to take the partial derivative of $f(x,y) = x\ln(x) + y\ln(y), x + y = 1$?

Published on 29 Apr 2026 - 6:48

List Question

for any $e$ prove that the difference between $f(x)$ and $f(x+e)$ is the same as the directional derivative of $f(x+te)$ in the direction of $e$

Show that $\left|\int_a^b f(x) dx\right|\leqslant \frac{M}{12}(b-a)^3$?

What is chain rule for second order derivative of a composite function?

Find the radius of a cylinder of given volume V if its surface area is a minimum.

Maximizing $f(x,y,z)$ over $\mathcal T=\left\{(x,y,z)\, |\, 0\leq y\leq x-1\, , \, x\in[1,2]\, , \, z\in\mathbb R \right\}$

Prove that a function has a root in interval, when you know, by Rolle, there is a root of the derivative, but you don't know it.

Prob. 7, Sec. 6.1, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: A necessary and sufficient condition for the existence of $\big(|f|\big)^\prime$

Find functions $f:\mathbb{R}^n\to\mathbb{R}, n\ge 2$ such that $\nabla f(x)= 0$ and $x$ is local min but not global, and $x$ is saddle point

How to reduce this to have only one x ...

Prob. 17, Sec. 6.1, in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: Straddle Lemma

Gradient of the maximum of smooth functions

Interesting Successive differentiation

Problem with Intuitive meaning of derivative

Second derivative finite difference of a convolution of two functions.

How to take the partial derivative of $f(x,y) = x\ln(x) + y\ln(y), x + y = 1$?

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