List questions from rolles-theorem

101

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Let $P (x )=x^4+ax^3+bx+c=0$ and have real coefficient and have all real roots . Prove that $ab \leq 0$

Published on 23 Feb 2026 - 9:32

97

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Generalization of Rolle's Theorem

Published on 23 Feb 2026 - 9:28

40

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a Mean Value Theorem Proof

Published on 23 Feb 2026 - 9:24

233

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Geometry of mean value theorem?

Published on 09 Apr 2026 - 16:22

969

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Root multiplicity for non-polynomial function

Published on 23 Feb 2026 - 9:24

124

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Rolle's and Lagrange's theorems in parametric equations

Published on 23 Feb 2026 - 9:27

71

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A function $g(x)$ has one and only one real root if $g'(x)\leq k <0$.

Published on 23 Feb 2026 - 9:29

249

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Given $f(x) = x \sin\frac1x$, find roots of $f'(x)$ in the interval $0\le x \le \frac 1{\pi}$.

Published on 23 Feb 2026 - 9:34

330

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Spivak, Calculus 3rd Ed. Chapter 11 problem 32

Published on 23 Feb 2026 - 9:34

125

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Some property of differentiable function

Published on 23 Feb 2026 - 9:26

134

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Rolle's theorem proof in Apostol: meaningfulness of interior

Published on 23 Feb 2026 - 9:32

341

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Application of Rolle's theorem and determinant

Published on 23 Feb 2026 - 9:29

57

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Is this inference from Rolle's Theorem correct?

Published on 23 Feb 2026 - 9:26

892

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Twice differentiable function on the closed interval $[a,b]$

Published on 23 Feb 2026 - 9:26

352

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Let a function f(x) be twice differentiable such that $ f(0) = 0, f(\pi/2)= 1 , f(3\pi/2)=-1$. To prove that there exists a ‘c’ in $ (0,3\pi/2)$

Published on 23 Feb 2026 - 9:32

List Question

Let $P (x )=x^4+ax^3+bx+c=0$ and have real coefficient and have all real roots . Prove that $ab \leq 0$

Generalization of Rolle's Theorem

a Mean Value Theorem Proof

Geometry of mean value theorem?

Root multiplicity for non-polynomial function

Rolle's and Lagrange's theorems in parametric equations

A function $g(x)$ has one and only one real root if $g'(x)\leq k <0$.

Given $f(x) = x \sin\frac1x$, find roots of $f'(x)$ in the interval $0\le x \le \frac 1{\pi}$.

Spivak, Calculus 3rd Ed. Chapter 11 problem 32

Some property of differentiable function

Rolle's theorem proof in Apostol: meaningfulness of interior

Application of Rolle's theorem and determinant

Is this inference from Rolle's Theorem correct?

Twice differentiable function on the closed interval $[a,b]$

Let a function f(x) be twice differentiable such that $ f(0) = 0, f(\pi/2)= 1 , f(3\pi/2)=-1$. To prove that there exists a ‘c’ in $ (0,3\pi/2)$

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