Let be a thrice continuously differentiable function.Prove or disprove that between two consecutive roots of there exist atmost roots of

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- November 14th 2008, 04:15 PMpankajApplication of derivatives
Let be a thrice continuously differentiable function.Prove or disprove that between two consecutive roots of there exist atmost roots of

- November 14th 2008, 05:47 PMNonCommAlg
- November 15th 2008, 05:19 AMpankaj
I had drawn the graph and I found that there are indeed 3 points but I am not able to apply Rolle's theorem.I doubt if converse of Rolle's theorem is true.

- November 15th 2008, 09:04 AMNonCommAlg
suppose are two consecutive zeros of suppose has 4 zeros such that then by Rolle's theorem there exist

such that again by Rolle's theorem there exist such that finally, again, by Rolle's theorem there exists such

that but obviously which contradicts our assumption that are two consecutive zeros of so can have at most 3 zeros between - November 15th 2008, 04:52 PMpankaj
Somehow I was missing point you made out inthe last sentence.

Nice proof.Graphical method on which I was working was not very convincing.