List questions from rolles-theorem

Published on 12 Apr 2026 - 5:37

95

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$2019f'(x)+2020f(x)\geq2021$

Published on 24 Feb 2026 - 10:14

88

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a little problem about Rolle theorem

Published on 11 Apr 2026 - 20:16

22

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How to do this question with the help of Rolle's theorm

Published on 12 Apr 2026 - 14:58

71

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Intuitive understanding for $f(x)=f'(x)$ in $(a,b)$ when $f(a)=f(b)=0$

Published on 12 Apr 2026 - 7:40

65

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If for $x\in(\frac{1}{2},\infty)$ we have $f'(x)=(e^x-1)(x-2)(x-3)$. Show that there exist exactly two roots of $f''(x)=0$ in the given domain

Published on 24 Feb 2026 - 10:19

226

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Prove that there exists $\xi \in (a,b)$ such that $f(a)-2f(\frac{a+b}{2})+f(b)=\frac{1}{4}(b-a)^2f''(\xi) .$

Published on 24 Feb 2026 - 10:19

99

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discovering Mean Value Theorem

Published on 12 Apr 2026 - 9:44

214

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On Rolle's Theorem

Published on 24 Feb 2026 - 10:12

316

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Show that a function has exactly one real root

Published on 11 Apr 2026 - 4:30

96

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Rolle' Theorem on Second Derivative

Published on 12 Apr 2026 - 6:05

228

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A function with positive $n$-th derivative has at most $n$ roots – an inequality version of the Fundamental theorem of Algebra.

Published on 15 Mar 2026 - 5:37

76

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A function with weakly positive $n$-th derivative has at most $n$ roots – an inequality version of the Fundamental theorem of Algebra.

Published on 15 Mar 2026 - 15:16

List Question

Application of Rolle's theorem (a corollary of the mean value theorem of differentiation)

$2019f'(x)+2020f(x)\geq2021$

a little problem about Rolle theorem

How to do this question with the help of Rolle's theorm

Intuitive understanding for $f(x)=f'(x)$ in $(a,b)$ when $f(a)=f(b)=0$

If for $x\in(\frac{1}{2},\infty)$ we have $f'(x)=(e^x-1)(x-2)(x-3)$. Show that there exist exactly two roots of $f''(x)=0$ in the given domain

Prove that there exists $\xi \in (a,b)$ such that $f(a)-2f(\frac{a+b}{2})+f(b)=\frac{1}{4}(b-a)^2f''(\xi) .$

discovering Mean Value Theorem

On Rolle's Theorem

Show that a function has exactly one real root

Rolle' Theorem on Second Derivative

A function with positive $n$-th derivative has at most $n$ roots – an inequality version of the Fundamental theorem of Algebra.

A function with weakly positive $n$-th derivative has at most $n$ roots – an inequality version of the Fundamental theorem of Algebra.

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