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Froggy Jumps
Froggy Jumps

APLICACION DE LA DERIVADA, MAXIMOS Y MINIMOS

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APLICACION DE LA DERIVADA, MAXIMOS Y MINIMOS

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Ayuda a la rana a cruzar el estanque respondiendo correctamente sobre derivadas! Hallarás la primera derivada, puntos críticos y comprobarás máximos y mínimos con la segunda derivada

Created by

Luis Aladino Panimboza
Luis Aladino Panimboza
Ecuador

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APLICACION DE LA DERIVADA, MAXIMOS Y MINIMOS
 

Froggy Jumps

APLICACION DE LA DERIVADA, MAXIMOS Y MINIMOSOnline version

Ayuda a la rana a cruzar el estanque respondiendo correctamente sobre derivadas! Hallarás la primera derivada, puntos críticos y comprobarás máximos y mínimos con la segunda derivada

by Luis Aladino Panimboza
1

Para iniciar la búsqueda de los puntos máximos y mínimos de la función f(x) = 2x^3 - 3x^2 - 12x + 7, ¿cuál es el valor correcto de su primera derivada?

2

Al igualar la primera derivada f'(x) = 6x^2 - 6x - 12 a cero y resolver la ecuación por factorización (x - 2)(x + 1) = 0, ¿cuáles son las raíces o puntos críticos obtenidos?

3

Si evaluamos la función original f(x) = 2x^3 - 3x^2 - 12x + 7 con el punto crítico x_1 = 2, obtenemos el valor de y = -13. ¿Qué coordenada se forma en el plano cartesiano?

4

Para determinar con certeza científica si un punto crítico es un máximo o un mínimo, derivamos por segunda vez. ¿Cuál es la segunda derivada de nuestra función f(x) = 2x^3 - 3x^2 - 12x + 7?

5

Al evaluar el punto x_2 = -1 en la segunda derivada, el resultado es -18 (un número negativo). Según el criterio matemático, esto significa que el punto P_2 = (-1, 14) es un:

 
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