Question

Halla la tasa de variación de cada funcion en el intervalo [-4,3] e indica si es positiva , negativa o nula A) f(x)=x2-2x+4 B) f(x)= -3x + 2 En rl ejercico A es x elevado al 2 o cuadrado

Answer 1

`A) \hspace{3}Rate\hspace{3}of\hspace{3}change=-5\hspace{3}Negative\\\\B)\hspace{3}Rate\hspace{3}of\hspace{3}change=-21\hspace{3}Negative`

Explanation:

Given a function
`f(x)`, we called the rate of change to the number that represents the increase or decrease that the function experiences when increasing the independent variable from one value "
`x_1`" to another "
`x_2`".

The rate of change of
`f(x)` between
`x_1` and
`x_2` can be calculated as follows:

`Rate\hspace{3}of\hspace{3}change=f(x_2)-f(x_1)`

For:

`f(x)=x^2-2x+4`

Let's find
`f(x_1)` and
`f(x_2)`, where:

`[x_1,x_2]=[-4,3]`

`f(x_1)=f(-4)=(-4)^2-2(4)+4=16-8+4=12\\f(x_2)=f(3)=(3)^2-2(3)+4=9-6+4=7`

So:

`Rate\hspace{3}of\hspace{3}change =7-12=-5\hspace{3}Negative`

And for:

`f(x)-3x+2`

Let's find
`f(x_1)` and
`f(x_2)`, where:

`[x_1,x_2]=[-4,3]`

`f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7`

So:

`Rate\hspace{3}of\hspace{3}change =-7-14=-21\hspace{3}Negative`

Translation:

Dada una función
`f(x)`, llamábamos tasa de variación al número que representa el aumento o disminución que experimenta la función al aumentar la variable independiente de un valor "
`x_1`" a otro "
`x_2`".

La tasa de variación de
`f(x)` entre
`x_1` y
`x_2`, puede ser calculada de la siguiente forma:

`Tasa\hspace{3}de\hspace{3}variacion=f(x_2)-f(x_1)`

Para:

`f(x)=x^2-2x+4`

Encontremos
`f(x_1)` y
`f(x_2)`, donde:

`[x_1,x_2]=[-4,3]`

`f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7`

Entonces:

`Tasa\hspace{3}de\hspace{3}variacion =7-12=-5\hspace{3}Negativa`

Y para:

`f(x)-3x+2`

Encontremos
`f(x_1)` y
`f(x_2)`, donde:

`[x_1,x_2]=[-4,3]`

`f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7`

Entonces:

`Tasa\hspace{3}de\hspace{3}variacion=-7-14=-21\hspace{3}Negativa`