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Rápidez de Cambio Promedio

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Rápidez de Cambio Promedio

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Cuestionario de funciones

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6ix
6ix
Colombia

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Rápidez de Cambio Promedio
 

Rápidez de Cambio PromedioOnline version

Cuestionario de funciones

by 6ix
1

Calcula la rapidez de cambio promedio de f en el intervalo [2,5] si f(2)=3 y f(5)=11. Usa (f(5)-f(2))/(5-2).

2

Si f(x)=2x+1, ¿cuál es la rapidez de cambio promedio entre x=0 y x=4?

3

La rapidez de cambio promedio entre a y b depende de:

4

Verdadero o falso: Si f(b)=f(a), la rapidez de cambio promedio entre a y b es 0.

5

Analiza este procedimiento: calcular (f(b)-f(a))/(b-a) sin conocer f(a) ni f(b). ¿Correcto o incorrecto?

6

Si f(x)=x^2, hallar la rapidez de cambio promedio entre x=1 y x=3.

7

Determine si la afirmación: la rapidez de cambio promedio es la pendiente de la cuerda que une (a,f(a)) y (b,f(b)).

8

Para f(x)=sin(x) calcular rapidez de cambio promedio entre x=0 y x=π/2.

9

Verdadero o falso: la rapidez de cambio promedio puede ser positiva, negativa o 0 dependiendo de f.

10

Si f(x)=e^x, rapidez de cambio promedio entre 0 y 1 es:

11

Determina si es correcto: entre a=-2 y b=2 para f(x)=x^3, la rapidez de cambio promedio es 0.

12

Si f(x)=3x, la rapidez de cambio promedio entre x= -5 y x=0 es:

13

Analiza: cambiar de a=1 a b=2 para f(x)=x^2+1, la rapidez de cambio promedio es 2. ¿Correcto?

14

Si f(x)=√x, rapidez de cambio promedio entre x=4 y x=9 es:

15

Verdadero o falso: una mayor diferencia (b-a) siempre aumenta la rapidez de cambio promedio.

16

Dado f(x)=x^2-4x, rapidez de cambio promedio entre a=1 y b=3 es:

17

Si f(x)=ln x, rapidez de cambio promedio entre x=1 y x=e es:

18

Verdadero o falso: la rapidez de cambio promedio es siempre una cantidad constante para una función dada.

19

Calcular rapidez de cambio promedio para f(x)=x^2 entre a=-1 y b=2.

20

La rapidez de cambio promedio entre a y b para f(x)=5 es:

21

Si f(x)=x^3 y a=0, b=2, la rapidez de cambio promedio es:

22

Analiza: en f(x)=sin x, rapidez entre 0 y π es:

23

Si f(x)=x^2+2x y a=0, b=3, rapidez de cambio promedio es:

24

Verdadero o falso: la rapidez de cambio promedio siempre mide cuánto cambia f por unidad de x.

25

26

27

Feedback

(11-3)/(5-2)=8/3 unidades por unidad de x.

Cambio promedio = (f(4)-f(0))/(4-0) = (9-1)/4 = 2.

Depende de f(a), f(b) y de la diferencia (b-a).

Si f(b)=f(a) entonces (f(b)-f(a))/(b-a)=0.

Se requieren f(a) y f(b) para la fórmula.

(f(3)-f(1))/(3-1)=(9-1)/2=4.

Es la pendiente de la cuerda entre esos puntos.

f(0)=0, f(π/2)=1, diferencia 1.

Puede ser positiva, negativa o 0 según f y el intervalo.

(f(1)-f(0))/(1-0)=(e-1)/1.

f(-2)=-8, f(2)=8; (8-(-8))/4=16/4=4.

(f(0)-f(-5))/(0-(-5))=(0-(-15))/5=15/5=3.

(f(2)-f(1))/(1) = (5-2)/1=3.

f(4)=2, f(9)=3; (3-2)/5=1/5.

No siempre; depende de cambios en f(a) y f(b).

f(3)=9-12=-3; f(1)=1-4=-3; ( -3 - (-3) )/2 = 0.

f(1)=0, f(e)=1; (1-0)/(e-1)=1/(e-1).

Puede variar si se cambia el intervalo.

f(2)=4, f(-1)=1; (4-1)/3=1.

Si f es constante, el cambio es 0.

(f(2)-f(0))/(2-0)=(8-0)/2=4.

f(0)=0, f(π)=0; velocidad 0.

f(3)=9+6=15; (15-0)/3=5.

Por definición, es (f(b)-f(a))/(b-a).

 
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