Question

Mean value theorem and Lp functions

score 39 · Answer 1 · 2023-10-25 15:41:42

39

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Mean value theorem and Lp functions

Published on 25 Oct 2023 - 15:41

score 59 · Answer 2 · 2023-10-30 14:30:08

59

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How to understand "as $x$ tends to $a$, value $c$ also tends to $a$" at the proof L'Hospital's Rule using Cauchy theorem?

Published on 30 Oct 2023 - 14:30

score 52 · Answer 3 · 2023-11-02 02:40:00

52

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Prove using Lagrange's Mean Value Theorem, $\frac{x^2}{2} > x - \ln(1 + x) > \frac{x^2}{2(1 + x)}$ for all $x>1$

Published on 02 Nov 2023 - 2:40

score 68 · Answer 4 · 2023-11-02 03:44:17

68

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Finding a constant for the mean value theorem

Published on 02 Nov 2023 - 3:44

score 61 · Answer 5 · 2023-11-05 22:28:31

61

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If we know a bound for the third derivative and 3 roots for a function, how can we derive its possible maximum value?

Published on 05 Nov 2023 - 22:28

score 70 · Answer 6 · 2026-02-23 20:04:41

70

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How to show that there exists $\xi \in (a,b)$ such that $f'(\xi)=\frac{f(\xi)-f(a)}{\xi-a}$

Published on 23 Feb 2026 - 20:04

score 49 · Answer 7 · 2023-11-29 22:42:47

49

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Bounded second derivative also bounds the function

Published on 29 Nov 2023 - 22:42

score 55 · Answer 8 · 2023-11-30 06:15:43

55

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MVT Problem : Prove $f^{'}(a)=\lim_{x\to{a}} f^{'}(x)$

Published on 30 Nov 2023 - 6:15

score 99 · Answer 9 · 2023-12-01 01:49:29

99

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Let $f$ be continuous on $[a,b]$ and differentiable on $(a,b)$. If $\lim_{x\to{a}} f^\prime(x)$ exists, show that $f$ is differentiable at $a$

Published on 01 Dec 2023 - 1:49

score 57 · Answer 10 · 2023-12-04 04:56:59

57

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Question regarding Mean value theorem and a monotonically increasing function $f'$

Published on 04 Dec 2023 - 4:56

score 244 · Answer 11 · 2023-12-09 19:39:25

244

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Proof of chain rule using mean value theorem

Published on 09 Dec 2023 - 19:39

score 46 · Answer 12 · 2023-12-12 10:28:48

46

Views

Ratio of a function and its integral inequalities

Published on 12 Dec 2023 - 10:28

score 255 · Answer 13 · 2023-12-19 22:14:44

255

Views

With some conditions on $f$, resolve the claim $|f(x)-f(y)|\le|x-y|$ for all $x,y\in[0,1]$.

Published on 19 Dec 2023 - 22:14

score 177 · Answer 14 · 2023-12-21 11:21:33

177

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If $\theta(h)$ is such that $f(3+h)-f(3) = hf'(3+\theta(h)h)$, what is $\lim_{h \to 0} θ(h)$?

Published on 21 Dec 2023 - 11:21

score 54 · Answer 15 · 2023-12-24 21:38:24

54

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Find functions $f(x)$ and $g(x)$ such that the following conditions are satisfied for all $x > 0$:

Published on 24 Dec 2023 - 21:38

List Question

Mean value theorem and Lp functions

How to understand "as $x$ tends to $a$, value $c$ also tends to $a$" at the proof L'Hospital's Rule using Cauchy theorem?

Prove using Lagrange's Mean Value Theorem, $\frac{x^2}{2} > x - \ln(1 + x) > \frac{x^2}{2(1 + x)}$ for all $x>1$

Finding a constant for the mean value theorem

If we know a bound for the third derivative and 3 roots for a function, how can we derive its possible maximum value?

How to show that there exists $\xi \in (a,b)$ such that $f'(\xi)=\frac{f(\xi)-f(a)}{\xi-a}$

Bounded second derivative also bounds the function

MVT Problem : Prove $f^{'}(a)=\lim_{x\to{a}} f^{'}(x)$

Let $f$ be continuous on $[a,b]$ and differentiable on $(a,b)$. If $\lim_{x\to{a}} f^\prime(x)$ exists, show that $f$ is differentiable at $a$

Question regarding Mean value theorem and a monotonically increasing function $f'$

Proof of chain rule using mean value theorem

Ratio of a function and its integral inequalities

With some conditions on $f$, resolve the claim $|f(x)-f(y)|\le|x-y|$ for all $x,y\in[0,1]$.

If $\theta(h)$ is such that $f(3+h)-f(3) = hf'(3+\theta(h)h)$, what is $\lim_{h \to 0} θ(h)$?

Find functions $f(x)$ and $g(x)$ such that the following conditions are satisfied for all $x > 0$:

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