How Fermat found extrema
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866912805263769600 |
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| author | Skopenkov, A. |
| author_facet | Skopenkov, A. |
| contents | We present a short elementary proof of the well-known criterion for a cubic polynomial to have three real roots. The proof is based on Fermat's approach to calculus for polynomials. This approach illustrates the idea of a derivative rigorously but without technical $\varepsilon$-$δ$ language. The note is accessible to high-school students. An English version is followed by a more detailed Russian version. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1610_05968 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | How Fermat found extrema Skopenkov, A. History and Overview 01A45, 00A06, 00A09, 00A35 We present a short elementary proof of the well-known criterion for a cubic polynomial to have three real roots. The proof is based on Fermat's approach to calculus for polynomials. This approach illustrates the idea of a derivative rigorously but without technical $\varepsilon$-$δ$ language. The note is accessible to high-school students. An English version is followed by a more detailed Russian version. |
| title | How Fermat found extrema |
| topic | History and Overview 01A45, 00A06, 00A09, 00A35 |
| url | https://arxiv.org/abs/1610.05968 |