Criterio de la Segunda Derivada para la determinación de extremos locales para las funciones de dos variables

Teorema del Criterio de la Segunda derivada para la determinación de extremos locales para funciones de dos variables
[justify][/justify][size=150][justify]Sea [math]f:U\subseteq\mathbb{R}^2\longrightarrow\mathbb{R}[/math] una función definifa en el conjunto abierto [math]U[/math] de [br][math]\mathbb{R}^n[/math] tal que en una bola B con centro en el punto [math]\left(x_0,y_0\right)\in U[/math] sus derivadas parciales de segundo orden son continuas. Sea[br] 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[/img][br][/justify][list][*]Si [math]B^2-AC<0[/math] y [math]A>0[/math], entonces la función tiene un mínimo relativo [math]\left(x_0,y_0\right)[/math][br][/*][*]Si [math]B^2-AC<0[/math] y [math]A<0[/math], entonces la función tiene un máximo relativo en [math]\left(x_0,y_0\right)[/math][br][/*][*]Si [math]B^2-AC>0[/math], entonces la función tiene un punto silla en [math]\left(x_0,y_0\right)[/math][br][/*][*]Si [math]B^2-AC=0[/math], no se puede determinar la naturaleza del punto crítico. [/*][/list][br][justify]Para resolver el ejercicio que mostramos, el primer paso es calcular los puntos críticos, es por eso que calculamos las derivadas parciales de la función y las igualamos a cero. Tenemos que nuestro punto crítico es [math]p=\left(\frac{36}{23},-\frac{29}{33}\right)[/math], después aplicamos el criterio de la segunda derivada que explicamos previamente, calculando el valor de A, B y C, para finalmente realizar [math]B^2-AC[/math] y determinar la naturaleza del punto crítico. [br]Como el valor de [math]B^2-AC>0[/math], podemos decir que la función tiene un punto silla en [math]p=\left(\frac{36}{23},\frac{-29}{33}\right)[/math][/justify]. [/size]

Information: Criterio de la Segunda Derivada para la determinación de extremos locales para las funciones de dos variables