Derivadas
Páginas: 7 (1619 palabras)
Publicado: 20 de noviembre de 2012
1)[pic]
[pic]
[pic]
[pic] Rpta.
2)[pic]
[pic]
[pic]
[pic]
[pic] Rpta.
3)[pic]
No se cumple pues [pic]
[pic]
4)[pic]
[pic]No cumple[pic]
[pic] no cumple
5)[pic]
[pic]
[pic]
[pic]
[pic] Rpta.
[pic]
[pic] Rpta.
7)[pic]
[pic]
[pic]
[pic]
[pic]
8)[pic]
[pic][pic]
9)[pic]
[pic]
[pic]
10) [pic]
[pic]
11) [pic]
[pic]
[pic]
12)[pic]
[pic]
[pic]
13) Sea f(x)=a[pic]+bx+c, x[pic] donde a,b,c son constantes. Muestre que [pic] satisface el teorema del valor medio.
[pic]
[pic]
[pic] Rpta.
14) Muestre que la ecuación [pic] no puede tenr dos raíces distintas en l intervalo [pic].[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
15)[pic]
[pic] Puntos críticos x=0 x=[pic]3
16)[pic]
[pic]
[pic]
17) [pic]
[pic]
[pic]
[pic]
18)[pic]
[pic]
[pic]=0
19)[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
21)[pic]
[pic][pic]
22)[pic]
[pic]
[pic]
23)[pic]
[pic]
[pic]
[pic]
24)[pic]
[pic]+(1-x[pic]
[pic]
25)[pic]
[pic]
[pic] NO [pic] EXTREMOS
[pic]
[pic]
[pic]
27.-[pic]
[pic]
- +
[pic] punto minimo
28.-[pic]
[pic]
[pic]
[pic] puntomaximo
29.-[pic]
[pic]
[pic]
[pic] punto maximo
Punto mínimo
30.-[pic]
[pic]
[pic]
[pic]
Máximo=[pic]
Mínimo=[pic]
31.-[pic]
[pic]
[pic]
[pic]
Minimo dicontinuo
32.-[pic]
[pic]
+-
[pic] punto maximo
33.-[pic]
[pic]
+[pic]
[pic] minimo
34.-[pic]
[pic]
[pic]
+[pic]
[pic] minimo
35.-[pic]
[pic]
+[pic]
0. 1
Maximo minimo36.-[pic]
[pic]
[pic]
[pic]
Max min max
En los ejercicos 37 al 44, halle los avlores maximos y minimos absolutos de las funciones en los intervalos que se indican.
37.-[pic]
[pic] [pic]
[pic]
+ - + [pic]0 max 1min
F(0)=5 F(1)=3
38.-[pic]
[pic]
[pic] NO TIENE PUNTOS CRITICOS
[pic]
39. [pic]
[pic]
[pic]
[pic] + + - +
0 1 3
[pic]
[pic]
[pic]
[pic]
[pic]
40. [pic]
[pic]
[pic]
41.[pic]
[pic][pic]
[pic] [pic]
42.[pic]
[pic]
[pic]
- + [pic]
43. [pic]
[pic]
- + - + [pic]
0 1 2 [pic]
Max..
44. [pic]
[pic]
[pic]
[pic]
45. [pic]
Solución: [pic]
[pic]
[pic]
- - + [pic]
-1 (max.) 1(min.)
[pic]
[pic]
46. determine el punto P de la curva [pic]que este mas próximo al punto (7,0). Si P es tal punto,pruebe que la recta que pasa por (0,7) y P es normal a la curva en P .
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
- 1 + [pic]
Mínimo
47. se necesita construir en embudo cónico que tenga la generatriz igual a 20cm. ¿Cuál debe ser la altura del embudo para que su volumen sea el mayor posible?
[pic]
[pic]
[pic]
[pic] [pic]
[pic]
[pic]...
[pic]
[pic]
[pic] Rpta.
2)[pic]
[pic]
[pic]
[pic]
[pic] Rpta.
3)[pic]
No se cumple pues [pic]
[pic]
4)[pic]
[pic]No cumple[pic]
[pic] no cumple
5)[pic]
[pic]
[pic]
[pic]
[pic] Rpta.
[pic]
[pic] Rpta.
7)[pic]
[pic]
[pic]
[pic]
[pic]
8)[pic]
[pic][pic]
9)[pic]
[pic]
[pic]
10) [pic]
[pic]
11) [pic]
[pic]
[pic]
12)[pic]
[pic]
[pic]
13) Sea f(x)=a[pic]+bx+c, x[pic] donde a,b,c son constantes. Muestre que [pic] satisface el teorema del valor medio.
[pic]
[pic]
[pic] Rpta.
14) Muestre que la ecuación [pic] no puede tenr dos raíces distintas en l intervalo [pic].[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
15)[pic]
[pic] Puntos críticos x=0 x=[pic]3
16)[pic]
[pic]
[pic]
17) [pic]
[pic]
[pic]
[pic]
18)[pic]
[pic]
[pic]=0
19)[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
21)[pic]
[pic][pic]
22)[pic]
[pic]
[pic]
23)[pic]
[pic]
[pic]
[pic]
24)[pic]
[pic]+(1-x[pic]
[pic]
25)[pic]
[pic]
[pic] NO [pic] EXTREMOS
[pic]
[pic]
[pic]
27.-[pic]
[pic]
- +
[pic] punto minimo
28.-[pic]
[pic]
[pic]
[pic] puntomaximo
29.-[pic]
[pic]
[pic]
[pic] punto maximo
Punto mínimo
30.-[pic]
[pic]
[pic]
[pic]
Máximo=[pic]
Mínimo=[pic]
31.-[pic]
[pic]
[pic]
[pic]
Minimo dicontinuo
32.-[pic]
[pic]
+-
[pic] punto maximo
33.-[pic]
[pic]
+[pic]
[pic] minimo
34.-[pic]
[pic]
[pic]
+[pic]
[pic] minimo
35.-[pic]
[pic]
+[pic]
0. 1
Maximo minimo36.-[pic]
[pic]
[pic]
[pic]
Max min max
En los ejercicos 37 al 44, halle los avlores maximos y minimos absolutos de las funciones en los intervalos que se indican.
37.-[pic]
[pic] [pic]
[pic]
+ - + [pic]0 max 1min
F(0)=5 F(1)=3
38.-[pic]
[pic]
[pic] NO TIENE PUNTOS CRITICOS
[pic]
39. [pic]
[pic]
[pic]
[pic] + + - +
0 1 3
[pic]
[pic]
[pic]
[pic]
[pic]
40. [pic]
[pic]
[pic]
41.[pic]
[pic][pic]
[pic] [pic]
42.[pic]
[pic]
[pic]
- + [pic]
43. [pic]
[pic]
- + - + [pic]
0 1 2 [pic]
Max..
44. [pic]
[pic]
[pic]
[pic]
45. [pic]
Solución: [pic]
[pic]
[pic]
- - + [pic]
-1 (max.) 1(min.)
[pic]
[pic]
46. determine el punto P de la curva [pic]que este mas próximo al punto (7,0). Si P es tal punto,pruebe que la recta que pasa por (0,7) y P es normal a la curva en P .
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
- 1 + [pic]
Mínimo
47. se necesita construir en embudo cónico que tenga la generatriz igual a 20cm. ¿Cuál debe ser la altura del embudo para que su volumen sea el mayor posible?
[pic]
[pic]
[pic]
[pic] [pic]
[pic]
[pic]...
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