List questions from rolles-theorem

Published on 02 Jan 2021 - 5:21

70

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If $f \in \mathbf{C}^n(\mathbf{R})$ and $f(x_{0})=...=f(x_{n}) = 0$ for $x_{0} < ... < x_{n}$ then $f^{n}(\xi)=0$ for some $\xi \in (x_{0},x_{n})$

Published on 15 Jan 2021 - 2:56

100

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Calculus - Rolle question

Published on 15 Jan 2021 - 15:07

60

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Proving that an equation has exactly two solutions in the reals

Published on 16 Jan 2021 - 11:43

234

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How to prove the existence of exactly one root of a function in between two consecutive roots of another function

Published on 17 Jan 2021 - 5:00

76

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$f$ differentiable. Show there's $c\in(0,\infty)$ so that $f^{\prime}(c)=0$

Published on 17 Jan 2021 - 9:38

53

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Proof regarding Rolle's and Intermediate value theorems.

Published on 17 Jan 2021 - 12:41

42

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A problem on construction of a function

Published on 21 Jan 2021 - 9:31

65

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Rolle theorem for the Number of roots of a real function

Published on 27 Jan 2021 - 10:05

29

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Application of Mean Value Theorem on 2 differentiable functions simultaneously

Published on 27 Jan 2021 - 10:54

109

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statement about continuous function - false, why?

Published on 03 Feb 2021 - 3:48

209

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Proving that there are 3 solutions at most $f(x)=e^x-(ax^2+bx+c)$

Published on 17 Feb 2021 - 14:36

75

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Local minima of the modulus of a square-free complex polynomial is always zero?

Published on 03 Mar 2021 - 11:59

87

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Rolle-like problem

Published on 16 Mar 2021 - 13:52

108

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If $a$ and $b$ are consecutive roots of $f$, show that $f'(a)\cdot f'(b)\leq 0.$

Published on 26 Mar 2021 - 16:52

List Question

Analysing function at $x=0$

If $f \in \mathbf{C}^n(\mathbf{R})$ and $f(x_{0})=...=f(x_{n}) = 0$ for $x_{0} < ... < x_{n}$ then $f^{n}(\xi)=0$ for some $\xi \in (x_{0},x_{n})$

Calculus - Rolle question

Proving that an equation has exactly two solutions in the reals

How to prove the existence of exactly one root of a function in between two consecutive roots of another function

$f$ differentiable. Show there's $c\in(0,\infty)$ so that $f^{\prime}(c)=0$

Proof regarding Rolle's and Intermediate value theorems.

A problem on construction of a function

Rolle theorem for the Number of roots of a real function

Application of Mean Value Theorem on 2 differentiable functions simultaneously

statement about continuous function - false, why?

Proving that there are 3 solutions at most $f(x)=e^x-(ax^2+bx+c)$

Local minima of the modulus of a square-free complex polynomial is always zero?

Rolle-like problem

If $a$ and $b$ are consecutive roots of $f$, show that $f'(a)\cdot f'(b)\leq 0.$

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