How Fermat found extrema

A. Skopenkov

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arXiv · 1610.05968

How Fermat found extrema

A. Skopenkov

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Abstract

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 $\varepsilon$-$\delta$ language. The note is accessible to high-school students. An English version is followed by a more detailed Russian version.

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A. Skopenkov. 2016-10-19. How Fermat found extrema. https://arxiv.org/abs/1610.05968

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