1 2 18 25 1 2 2 3 1 2 4 3 1 2 3 1 2 f 4 f 1 f 0 f 3 f x x x x x x 16 8 6 16 8 1

1 2 18 25 1 2 2 3 1 2 4 3 1 2 3 1 2 f 4 f 1 f 0 f 3 f

This preview shows page 476 - 480 out of 640 pages.

1 2 18 25 , 1 2 2 , 3 1 2 , 4 3 1 0 2 3 1 2 f ' (–4) > 0 f ' ( 1) > 0 f ' (0) < 0 f ' (3) < 0 f x x x x x x ' ( ) ( ) = + = = − 16 8 6 16 8 0 1 2 2 2 3 1 2 , Derivada de una función
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477 Punto de corte con los ejes: (0, 0) f ' ( x ) < 0 f ( x ) es decreciente en ( , 1) ( 1, 4) (4, + ). La función no tiene máximos ni mínimos. b) Dom f = { 1} es una asíntota vertical. es una asíntota horizontal. Al tener asíntota horizontal, la función no tiene asíntota oblicua. Punto de corte con el eje Y : (3, 0) f ' ( x ) > 0 si x < 1 f ( x ) es creciente en ( , 1). f ' ( x ) < 0 si x > 1 f ( x ) es decreciente en ( 1, + ). La función no tiene máximos ni mínimos. Y X 1 1 f ( x ) f x x x x x x x x x ' ( ) ( )( ) ( )( ) ( = + + + + + + + 2 2 2 1 2 3 2 2 2 2 2 2 + = + + = = − ∉ 1 4 4 2 1 4 4 0 1 2 2 2 ) ( ) x x x x x f Dom lim x x x x y x + + + + + = = 2 2 2 3 2 1 1 1 lim x x x x lim x x x x x + + + + + = + + + + 1 2 2 1 2 2 2 3 2 1 2 3 2 1 1 x x + = + = − Y X 2 2 f ( x ) f x x x x x x x x x x ' ( ) ( ) ( ) ( = = 2 2 2 2 2 3 4 2 3 3 4 4 3 4 2 ) 10 SOLUCIONARIO
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478 c) Dom f = { 1, 4} es una asíntota vertical. es una asíntota vertical. es una asíntota horizontal. Al tener asíntota horizontal, la función no tiene asíntota oblicua. Punto de corte con el eje X : ( 5, 0) Punto de corte con el eje Y : f ( x ) es creciente en ( 11, 1) ( 1, 1) y es decreciente en ( , 11) (1, 4) (4, + ). Mínimo: Máximo: (1, 1) d) Dom f = {0} es una asíntota vertical. es una asíntota horizontal. Al tener asíntota horizontal, la función no tiene asíntota oblicua. lim x x x y x + + + = = 2 2 4 2 1 1 lim x x x lim x x x x x 0 2 2 0 2 2 4 2 4 2 + + + = + + + = + = x 0 Y X 6 2 f ( x ) 11 1 25 , f ' ( 2) > 0 f ' (0) > 0 f ' (3) < 0 f ' (5) < 0 12 11 2 1 0 1 4 5 f ' ( 12) < 0 3 f x x x x x x x x x ' ( ) ( )( ) ( ) = + = 2 2 2 2 3 4 5 2 3 3 4 10 + + = 11 3 4 10 11 3 4 0 10 2 2 2 2 2 2 ( ) ( ) x x x x x x x x x x + = = − = 11 0 11 1 0 5 4 , lim x x x y x + + = = 5 3 4 0 0 2 lim x x x lim x x x x x 4 2 4 2 5 3 4 5 3 4 + + = − + = + = x 4 lim x x x x x lim x x x + + = + + = − 1 2 1 2 5 3 4 5 3 4 = − x 1 Derivada de una función
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479 Puntos de corte con el eje X : f ( x ) es decreciente en ( , 1) (0, + ) y es creciente en ( 1, 0). Mínimo: ( 1, 1) e) Dom f = { 3, 2} es una asíntota vertical.
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