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F(x) =1x2+x-6
1- DOMINIO:
R-{-3 ,2 }
2- INTERSECCION CON LOS EJES “X” “Y”

∩X=(X-2)(X+3)

∩Y=-16
3- CRECIMIENTO Y DECRECMIENTO.
F(x)= 1´X2+X-6-1X2+X-6´(X2+X-6)2

F´(x)=X2+X-6-12x+1(X2+X-6)2

F(x)= x2+x-6-2x+1(X2+X-6)2

F(x)= -2x-1(X2+X-6)2

Pts críticos: x1= 2,80 x2=-1,80
-oo -3 -1/2 02 +oo
ceros | | | | | |
F´(x) | - | - | + | + | + |
F(x) | | | | | |

-oo-1/2 +oo
| | |
(x-1/2) | - | + |
(x2+x-6)2 | + | + |
F´(x) | - | + |
|

4. CONCAVIDAD.
F´´(x) = -2X-1(X2+X-6)2

F´´(x) =-2X-1´(X2+X-6)2-2(-2X-1)(X2+X-6)´(X2+X-6)4

F´´(x) = -2(X2+X-6)2+(4X+2)(2x+1)´(X2+X-6)3

F´´(x) = -2x2+2x+12+8x2+4x+4x+2(X2+X-6)3

F´´(x) = 2(3x2+3x+7)(X2+X-6)3
- oo -3 02 +o o
| | | | |
2 | + | + | + | + |
(3x2+3x+7) | + | + | + | + |
(x-2) | - | - | - | + |
(x+3) | - | + | + | + |
2(3x2+3x+7)(X2+X-6)3 | + | - | - | + || ∪ | ∩ | ∩ | ∪ |

-oo -3 -1/2 0 2 +oo
| | | | | |
F´(x) | - | - |+ | + | + |
F´´(x) | + | - | - | + | + |
F(x) | ∪ | ∩ | ∩ | ∩ | ∪ |

6. CUADRO DE VARIACIONES.
-oo -3 -1/2 o 3 +oo
| | | | | |
F´(x) | - |- | + | + | + |
F´´(x) | + | - | - | - | + |
F(x) | ∪ | ∩ | ∩ | ∩ | ∪ |
| | | | | |

5. ASINTOTAS.
* Verticales.
limn→-3+1 x2+x-6= +∞

limn→-3-1 x2+x-6= -∞

limn→2+1x2+x-6= +∞

limn→2-1 x2+x-6= -∞

* Horizontales
limn→+∞1 x2+x-6=0

limn→-∞1 x2+x-6=0

* Oblicuas

m= f(x)x y=mx + b

m =1x2+x-6x
m = 1x(2x-1)

7....