List questions from rolles-theorem

Published on 19 Nov 2017 - 0:48

49

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Proving the existence of a point in real analysis

Published on 19 Nov 2017 - 2:22

122

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Proving existence of points in a twice differentiable function

Published on 20 Nov 2017 - 2:37

56

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Find a constant $M$ so that $|f(x) - f(a)|\leq M(x - a)^2.$

Published on 27 Nov 2017 - 2:48

4.4k

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Using Rolle's theorem and IVT, show that $x^4-7x^3+9=0$ has exactly $2$ roots.

Published on 24 Dec 2017 - 14:01

1.3k

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Prove f(x) > 0 for all x > 0

Published on 02 Jan 2018 - 15:51

6.3k

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How to show that an equation has exactly two solutions?

Published on 06 Jan 2018 - 11:50

105

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A problem on Rolle's theorem

Published on 28 Aug 2020 - 8:06

97

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Rolle's theorem: Show that there is a sequence $(a_{n})$ such that $\forall n \geq 1$, $f^{(n)}(a_{n}) = 0$.

Published on 02 Sep 2020 - 19:33

196

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A degree $n$ polynomial can have at most $n$ real zeroes.

Published on 06 Sep 2020 - 2:03

70

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Choosing correct options for the function $g(x)=\bigl(f(x)\bigr)^2+\bigl(f'(x)\bigr)^2$

Published on 20 Sep 2020 - 17:43

265

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How does this speed limit question work?

Published on 23 Sep 2020 - 6:36

44

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prove using Rolle or otherwise the existence of tangent through the origin given conditions

Published on 26 Sep 2020 - 14:46

111

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Parametric equation proof

Published on 27 Sep 2020 - 12:25

118

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Application of Rolle's theorem in a problem

Published on 05 Oct 2020 - 22:46

List Question

Proof using Rolle's theorem

Proving the existence of a point in real analysis

Proving existence of points in a twice differentiable function

Find a constant $M$ so that $|f(x) - f(a)|\leq M(x - a)^2.$

Using Rolle's theorem and IVT, show that $x^4-7x^3+9=0$ has exactly $2$ roots.

Prove f(x) > 0 for all x > 0

How to show that an equation has exactly two solutions?

A problem on Rolle's theorem

Rolle's theorem: Show that there is a sequence $(a_{n})$ such that $\forall n \geq 1$, $f^{(n)}(a_{n}) = 0$.

A degree $n$ polynomial can have at most $n$ real zeroes.

Choosing correct options for the function $g(x)=\bigl(f(x)\bigr)^2+\bigl(f'(x)\bigr)^2$

How does this speed limit question work?

prove using Rolle or otherwise the existence of tangent through the origin given conditions

Parametric equation proof

Application of Rolle's theorem in a problem

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