List questions from rolles-theorem

Published on 16 May 2023 - 17:48

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Solve problems of the form "given a differentiable function prove that there exists a point c such that"

Published on 23 Feb 2026 - 16:41

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Prove $x^2 + x \cos (x) -2 \cos ^2 (x) = 0$ has exactly two real roots

Published on 08 Jun 2023 - 13:17

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How to choose functions in proofs type Rolle?

Published on 08 Sep 2023 - 1:08

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Is this proof of Rolle's Theorem a valid one?

Published on 20 Sep 2023 - 7:35

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How to proof the derivative is continuous

Published on 29 Sep 2023 - 18:39

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Rolle's Theorem in proving exactly one real zero

Published on 07 Nov 2023 - 2:11

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Using Rolle's Theorem to prove roots

Published on 20 Nov 2023 - 15:54

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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 21 Nov 2023 - 15:30

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Finding another root to apply Rolle's theorem.

Published on 26 Nov 2023 - 2:51

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Rolle's theorem?

Published on 01 Dec 2023 - 16:08

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Rolle's theorem: if $f(0)=f(\pi)=0$ then $f'(c)=\tan(f(c))$ for some $c$.

Published on 15 Dec 2023 - 10:21

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Let $f$ be continuous in $[0,2]$ and differentiable in $(0,2)$ such that $|f'(x)|\leqslant1$ and $f(0)=1=f(2)$. Prove that $f(x)\geqslant0$.

Published on 27 Dec 2023 - 21:55

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Is there a missing assumption in this problem?

Published on 11 Jan 2024 - 7:08

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Assumptions underlying Rolle's Theorem

Published on 30 Jan 2024 - 17:24

List Question

Trigonometric proof with calculus

Solve problems of the form "given a differentiable function prove that there exists a point c such that"

Prove $x^2 + x \cos (x) -2 \cos ^2 (x) = 0$ has exactly two real roots

How to choose functions in proofs type Rolle?

Is this proof of Rolle's Theorem a valid one?

How to proof the derivative is continuous

Rolle's Theorem in proving exactly one real zero

Using Rolle's Theorem to prove roots

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

Finding another root to apply Rolle's theorem.

Rolle's theorem?

Rolle's theorem: if $f(0)=f(\pi)=0$ then $f'(c)=\tan(f(c))$ for some $c$.

Let $f$ be continuous in $[0,2]$ and differentiable in $(0,2)$ such that $|f'(x)|\leqslant1$ and $f(0)=1=f(2)$. Prove that $f(x)\geqslant0$.

Is there a missing assumption in this problem?

Assumptions underlying Rolle's Theorem

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