In the field of arithmetic there was a famous French mathematician named Pierre de Fermat, who stated for the first time in 1637 a theorem which was as follows: “if a function f reaches a local maximum or minimum in c, and if the Derivative f´ (c) exists at point c then f´ (c) = 0. This theorem is usually applied to find local maxima and minima of differentiable functions in open intervals, since they are all stationary points of the function, that is, they are those points where the derived function is equal to zero (f´ (x) = 0).
Fermat's theorem only provides a necessary condition for local maximums and minimums, although it does not explain another class of stationary points, such as inflection points in some cases, however the second derivative of the function (f´´) (if actually exists) can tell whether the stationary point is a maximum, a minimum, or an inflection point.
For mathematics, a theorem represents a proposition that, starting from a hypothesis, states a truth that cannot be explained by itself, Fermat's theorem is a thesis with a simple and achievable statement, however, in order to be solved, the most mathematical methods were needed. 20th century complexes.
This theorem was found 5 years after the death of Fermat (1665) by his son, he got it noted in the margin of a book of arithmetic by Diophantus of Alexandria. Since that time many have wanted to solve it, even large sums of money have been offered for those who managed to decipher it.
