what is the behavior of the graph y =-x^3-5x^2-3+9 at each of its zeros

Answers

Answer 1

The behavior of the graph of the function y = -x^3 - 5x^2 - 3x + 9 at each of its zeros is as follows:

At x ≈ -4.919 and x ≈ -0.488, there are local minima.

At x ≈ 1.752, there is a local maximum.

Let's analyze the behavior of the graph of the function y = -x^3 - 5x^2 - 3x + 9 at each of its zeros in more detail.

To find the zeros of the function, we need to solve the equation -x^3 - 5x^2 - 3x + 9 = 0.

To simplify the calculations, let's use a numerical method like the Newton-Raphson method to approximate the zeros. We'll start with initial guesses and iteratively refine them to improve the accuracy of the solutions.

Initial guess: x_0 ≈ -5

Applying the Newton-Raphson method:

x_1 = x_0 - f(x_0) / f'(x_0)

where f(x) = -x^3 - 5x^2 - 3x + 9

f'(x) = -3x^2 - 10x - 3 (derivative of f(x))

x_1 = -5 - (-5^3 - 5(-5)^2 - 3(-5) + 9) / (-3(-5)^2 - 10(-5) - 3)

≈ -4.919

Initial guess: x_0 ≈ -1

Applying the Newton-Raphson method:

x_1 = x_0 - f(x_0) / f'(x_0)

x_1 = -1 - (-1^3 - 5(-1)^2 - 3(-1) + 9) / (-3(-1)^2 - 10(-1) - 3)

≈ -0.488

Initial guess: x_0 ≈ 2

Applying the Newton-Raphson method:

x_1 = x_0 - f(x_0) / f'(x_0)

x_1 = 2 - (2^3 - 5(2)^2 - 3(2) + 9) / (-3(2)^2 - 10(2) - 3)

≈ 1.752

After iterating through the Newton-Raphson method, we approximate the zeros as follows:

x ≈ -4.919

x ≈ -0.488

x ≈ 1.752

Now, let's analyze the behavior of the graph at each zero:

x ≈ -4.919:

When x is close to -4.919, y is close to zero. Since the coefficient of the leading term (-x^3) is negative, as x approaches -4.919 from the left side, the graph of the function will be decreasing. As x approaches -4.919 from the right side, the graph will be increasing. Therefore, the behavior of the graph near x ≈ -4.919 is a local minimum.

x ≈ -0.488:

When x is close to -0.488, y is close to zero. Similarly, as x approaches -0.488 from the left side, the graph will be decreasing, and as x approaches -0.488 from the right side, the graph will be increasing. Therefore, the behavior of the graph near x ≈ -0.488 is also a local minimum.

x ≈ 1.752:

When x is close to 1.752, y is close to zero. In this case, as x approaches 1.752 from the left side, the graph will be increasing, and as x approaches 1.752 from the right side, the graph will be decreasing. Therefore, the behavior of the graph near x ≈ 1.752 is a local maximum.

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What Is The Behavior Of The Graph Y =-x^3-5x^2-3+9 At Each Of Its Zeros

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A solid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown.



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Answer:

A

Step-by-step explanation:

What is the domain of the function y = l n (x + 2)
A. x < -2
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Answers

Answer:

Option B.

Step-by-step explanation:

For a function f(x), the domain is the set of all the possible values of x that can be used in the function.

We know that the natural logarithm is only defined for positive real numbers.

So, the function:

Ln(x + 2)

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To isolate x, we just need to subtract 2 in both sides of the inequality.

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This is the domain of the function.

The correct option is B.

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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What is the vertex of the graph of the function f(x) = x^2 + 8x - 2?

Answers

Answer:

(-4,-18)

Step-by-step explanation:

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Step-by-step explanation:

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Dentro de 15 años la edad de Carlos será el doble de la edad de Ana. Hace 6 años la edad de Carlos era el triple de la de Ana. Calcular la suma de sus edades y dar como respuesta la suma de cifras de este resultado

Answers

Answer:

Ana tiene 27 años mientras que Carlos, tiene 69 años

La suma de las edades es: 27+69 = 96

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Step-by-step explanation:

Vamos a hacer una linea temporal para ubicarnos en tiempo.

AÑO 2021, Ana tiene una edad A mientras que Carlos tiene una edad C

15 años para adelante

AÑO 2036, la edad de Carlos es el doble de la de Ana

C = 2A

Si nos vamos 6 años para atrás

AÑO 2015, la edad de Carlos es el triple de la de Ana

C = 3A

Como de 2015 a 2036 pasan 21 años, podemos plantear que

La edad de Carlos + 21  va a ser 2 veces la edad de Ana, traducido:

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Si Ana en 2014 tiene 21 años, Carlos tiene 63 (el triple) por lo que sumamos 6 años y llegamos al presente:

En 2021, Ana tiene 27 años (21+6), mientras que Carlos tiene 69 (63+6). Edades actuales.

Nos corremos 15 años al futuro, por lo que llegamos al año 2036.

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Answers

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Step-by-step explanation:

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The value of coefficient of correlation coefficient is -0.953 which is a negative correlation between x and y option (A) is correct.

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We have given data in the table.

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Answers

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Double everything to get to 4 servings and then half everything to get 1 serving. Add it all up!

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2 1/2 cup cheese

2 1/2 cup milk

10 potatoes

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Answers

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Answers

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Step-by-step explanation:

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z)

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Hope this helps!

Answer:

to find y

you find the bottom right angle

which is 180-120 = 60

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then 180 -95 because the sum of all angles in a triangle is 180

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Answers

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Answer:

Solution given:

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Answers

Answer:

C is infact correct

Step-by-step explanation:

Give guy above brainly

The experimental probability in simplest form that the number cube shows 6 will be 3/10.

What is probability ?

Probability is a branch of mathematics that deals with the occurrence of a random event.

According to the question

Dave rolled a number cube 10 times and recorded the frequency of each result in this table.

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so ,

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The experimental probability in simplest form that the number cube shows 6 will be 3/10.

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An experiment consists of spinning the spinners shown and adding the numbers together. Complete the array.

Answers

Answer:

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Step-by-step explanation:

Given

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Array:

[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {} & { } & { } & {5} & {2} & { } & {} & { } & { } & {3} & {4} & { } & {} & { } & {4} & { } & {6} & { } & {} \ \end{array}[/tex]

Required

Complete the blanks

To do this, we simply add up corresponding row and column elements.

[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {} & { } & { } & {5} & {2} & { } & {} & { } & { } & {3} & {4} & { } & {} & { } & {4} & { } & {6} & { } & {} \ \end{array}[/tex]

So, we have:

[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {1+1} & {1+2 } & {1+3 } & {4} & {2} & {2+1 } & {2+2} & {2+3 } & {2+4 } & {3} & {4} & {3+2 } & {3+3} & {3+4 } & {4} & {4+1 } & {6} & {4+3 } & {4+4} \ \end{array}[/tex]

Add

[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {2} & {3} & {4} & {5} & {2} & {3} & {4} & {5} & {6} & {3} & {4} & {5} & {6} & {7} & {4} & {5} & {6} & {6} & {8} \ \end{array}[/tex]

Sarah kept track of the points she scored during her first five basketball games in the table shown. easy help

Answers

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E

Step-by-step explanation:

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Which expression is equivalent to 16x4 – 64? and explain the answer plzz​

Answers

Answer:

4(4x1-16)

Hope this helps

Have a good day :)

PS I disibuted 4 to 4x1 to get 16 and 4 to -16 to get -64

Step-by-step explanation:

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