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2 years ago

3. If the line tangent to the graph of the function f at the point (1,7) also passes through the point

Mathematics

1 answer:

Usimov [2.4K]2 years ago

5 0

Answer:

f'(-1)= 3

Step-by-step explanation:

slope = (y2 - y1)/(x2 - x1)= (7-(-2))/(1-(-2))=9/3=3

Slope of the tangent line in the given point equals f' at this point.

So,

f'(-1)= 3

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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

masya89 [10]

Answer:

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

Step-by-step 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:

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

<em>Translation:</em>

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:

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

8 0

3 years ago

Is a number of television in a household a discrete quantitative or continuous quantitative

mezya [45]

discrete, you cannot have 1.5 televisions

generally the number of X is a discrete variable.

continous = can contain decimal value (float values)

discrete = no decimal (integers)

7 0

3 years ago

The two triangles are similar, what is the value of X?

Gennadij [26K]

Answer:

x=4

Step-by-step explanation:

Since both triangles are similar, you can make an equation 12/5x-2 = 16/6x. When you cross multiply you get 72x=80x-32. Then you transfer the 80x and you get -8x = -32. Then you divide by -8 and you get x=4.

7 0

3 years ago

Solve by setting up a system of linear equations with 2 variables and 2 unknowns. Two hundred seventy six students enrolled in a

jeyben [28]

Let us say ,

x=number of students who passed

y=number of students who failed

total number of students =276

x+y=276..................(1)

We are given 5 times the number of students passed as failed.

x=5y.............(2)

plugging value of x from (2) in (1),

5y+y=276

6y=276

y=46

x=5y=46*5=230

x=number of students who passed=230

4 0

3 years ago

$60. The selling price is $105 is 175% because $105 — $60 = 1.75

kramer

45℅ should be answer,...........

6 0

3 years ago