Question

(Re)Defining Rolle's theorem and its converse

score 68 · Answer 1 · 2024-02-05 04:55:42

68

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(Re)Defining Rolle's theorem and its converse

Published on 05 Feb 2024 - 4:55

score 95 · Answer 2 · 2024-03-08 08:20:00

95

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If $f(a)=b$ and $f(b)=a$. Prove that there exists at least one $c$ such that $|f'(c)|<1$. Also prove that ther exists some 'd' such that $|f'(d)|>1$

Published on 08 Mar 2024 - 8:20

score 52 · Answer 3 · 2024-03-14 11:58:23

52

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Differentiable $f: [0, 1] → \mathbb{R}: \int_{0}^{1} f(x)dx = \int_{0}^{1}xf(x)dx.$ Prove $\exists c \in (0, 1):f(c) = 2018\int_{0}^{c}f(x)dx$

Published on 14 Mar 2024 - 11:58

score 1.8k · Answer 4 · 2016-05-06 13:47:10

1.8k

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Find the value of $c$ which satisfies Rolle's Theorem for the function $f(x)=x^3-12x$ on the interval $[0,2\sqrt3]$.

Published on 06 May 2016 - 13:47

score 977 · Answer 5 · 2013-05-05 07:33:03

977

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Applying the Mean Value Theorem to conclude a function has a zero

Published on 05 May 2013 - 7:33

score 4.9k · Answer 6 · 2013-05-13 23:39:16

4.9k

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Using the Intermediate Value Theorem and Rolle's theorem to determine number of roots

Published on 13 May 2013 - 23:39

score 146.2k · Answer 7 · 2013-11-21 02:48:36

146.2k

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Prove using Rolle's Theorem that an equation has exactly one real solution.

Published on 21 Nov 2013 - 2:48

score 1.5k · Answer 8 · 2014-02-06 14:10:28

1.5k

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Rolle theorem on infinite interval

Published on 06 Feb 2014 - 14:10

score 58 · Answer 9 · 2017-04-27 18:00:42

58

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Proof of Rolle's Theorem: global max implies local max

Published on 27 Apr 2017 - 18:00

score 226 · Answer 10 · 2017-05-03 04:43:39

226

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Rolle's Theorem in reverse

Published on 03 May 2017 - 4:43

score 535 · Answer 11 · 2017-05-10 22:28:21

535

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Application of MVT for integrals

Published on 10 May 2017 - 22:28

score 88 · Answer 12 · 2017-05-12 10:05:33

88

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What does C mean when talking about range of functions?

Published on 12 May 2017 - 10:05

score 240 · Answer 13 · 2017-05-14 04:37:02

240

Views

$P_n(x):={1\over{2^n{n!}}}{d^n\over dx^n}[(x^2-1)^n]$ has N Distinct Root

Published on 14 May 2017 - 4:37

score 2.5k · Answer 14 · 2017-05-15 04:00:00

2.5k

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Prove an equation has exactly two real roots

Published on 15 May 2017 - 4:00

score 139 · Answer 15 · 2017-05-29 04:13:54

139

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Let $f$ be a polynomial with at least $k$ different roots, prove that $f'$ hast at least $k-1$ different roots

Published on 29 May 2017 - 4:13

List Question

(Re)Defining Rolle's theorem and its converse

If $f(a)=b$ and $f(b)=a$. Prove that there exists at least one $c$ such that $|f'(c)|<1$. Also prove that ther exists some 'd' such that $|f'(d)|>1$

Differentiable $f: [0, 1] → \mathbb{R}: \int_{0}^{1} f(x)dx = \int_{0}^{1}xf(x)dx.$ Prove $\exists c \in (0, 1):f(c) = 2018\int_{0}^{c}f(x)dx$

Find the value of $c$ which satisfies Rolle's Theorem for the function $f(x)=x^3-12x$ on the interval $[0,2\sqrt3]$.

Applying the Mean Value Theorem to conclude a function has a zero

Using the Intermediate Value Theorem and Rolle's theorem to determine number of roots

Prove using Rolle's Theorem that an equation has exactly one real solution.

Rolle theorem on infinite interval

Proof of Rolle's Theorem: global max implies local max

Rolle's Theorem in reverse

Application of MVT for integrals

What does C mean when talking about range of functions?

$P_n(x):={1\over{2^n{n!}}}{d^n\over dx^n}[(x^2-1)^n]$ has N Distinct Root

Prove an equation has exactly two real roots

Let $f$ be a polynomial with at least $k$ different roots, prove that $f'$ hast at least $k-1$ different roots

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