23) criterio de la primera derivada

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 Criterio de la primera derivada:

Ejemplo:

Hallar los máximos y mínimos de :

f(x)=12x

3

-30x

2

-247x+12

Como es una ecuación de tercer grado va a tener 2 máximos y/o mínimos. El

número de máximos y mínimos que tiene una ecuación está dado por el término

de mayor grado menos uno.

Pasos para aplicar el criterio de la primera derivada:

1.-Derivar f(x)

f’(x)=36x

2

-60x-24

2.-Igualar la derivada con cero (para que m=0 y ahí se cumpla un máximo o un

mínimo)

36x

2

-60x-24=0

3.-Hallar los valores críticos de la ecuación (no son raices solución porque

anteriormente derivé la ecuación)

4.-Los pongo en forma de factor (igualar cada uno a cero)

x-2=0

x+0.333=0

5.-Análisis de los valores críticos:

Para

x=2 voy a tomar un instante antes de 2 y uno después de 2

antes=1.9

después=2.1

1.9-2 (-)

(-)

1.9+.33 (+)

mínimo

333.0x

2x

)36(2

)24)(36)(4(360060

2

1

−=

=

=

−−

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 Criterio de la primera derivada: Ejemplo: Hallar los máximos y mínimos de : f(x)=12x3-30x2-247x+12 Como es una ecuación de tercer grado va a tener 2 máximos y/o mínimos. El número de máximos y mínimos que tiene una ecuación está dado por el término de mayor grado menos uno. Pasos para aplicar el criterio de la primera derivada: 1.-Derivar f(x) f’(x)=36x2-60x-24 2.-Igualar la derivada con cero (para que m=0 y ahí se cumpla un máximo o un mínimo) 36x2-60x-24=0 3.-Hallar los valores críticos de la ecuación (no son raices solución porque 60  3600 − ( 4 )( 36 )( −24) ...
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