Question

(Re)Defining Rolle's theorem and its converse

score 69 · Answer 1 · 2026-02-23 21:46:43

69

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(Re)Defining Rolle's theorem and its converse

Published on 23 Feb 2026 - 21:46

score 96 · Answer 2 · 2026-02-23 21:48:24

96

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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 23 Feb 2026 - 21:48

score 53 · Answer 3 · 2026-02-23 21:48:24

53

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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 23 Feb 2026 - 21:48

score 1.8k · Answer 4 · 2026-02-23 21:48:35

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 23 Feb 2026 - 21:48

score 978 · Answer 5 · 2026-02-23 21:43:34

978

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

Published on 23 Feb 2026 - 21:43

score 4.9k · Answer 6 · 2026-02-23 21:47:01

4.9k

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

Published on 23 Feb 2026 - 21:47

score 146.2k · Answer 7 · 2026-02-23 21:46:44

146.2k

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

Published on 23 Feb 2026 - 21:46

score 1.5k · Answer 8 · 2026-02-23 21:44:21

1.5k

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Rolle theorem on infinite interval

Published on 23 Feb 2026 - 21:44

score 59 · Answer 9 · 2026-02-23 21:47:01

59

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

Published on 23 Feb 2026 - 21:47

score 227 · Answer 10 · 2026-02-23 21:42:47

227

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Rolle's Theorem in reverse

Published on 23 Feb 2026 - 21:42

score 536 · Answer 11 · 2026-02-23 21:44:57

536

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Application of MVT for integrals

Published on 23 Feb 2026 - 21:44

score 89 · Answer 12 · 2026-02-23 21:45:30

89

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What does C mean when talking about range of functions?

Published on 23 Feb 2026 - 21:45

score 241 · Answer 13 · 2026-02-23 21:47:54

241

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

Published on 23 Feb 2026 - 21:47

score 2.5k · Answer 14 · 2026-02-23 21:46:54

2.5k

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Prove an equation has exactly two real roots

Published on 23 Feb 2026 - 21:46

score 140 · Answer 15 · 2026-02-23 21:48:14

140

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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 23 Feb 2026 - 21:48

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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