Find the 2nd Derivative:
f(x) = 3x⁴ + 2x² - 8x + 4

Answers

Answer 1

Answer:

[tex]f''(x)=36x^2+4[/tex]

Step-by-step explanation:

Let's start by finding the first derivative of [tex]f(x)= 3x^4+2x^2-8x+4[/tex]. We can do so by using the power rule for derivatives.

The power rule states that:

[tex]\frac{d}{dx} (x^n) = n \times x^n^-^1[/tex]

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

[tex]\frac{d}{dx} (3x^4+2x^2-8x+4)[/tex]

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

[tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)[/tex]

Simplify the equation.

[tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)[/tex] [tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)[/tex] [tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)[/tex][tex]f'(x)=12x^3+4x-8[/tex]

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

[tex]\frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)[/tex] [tex]\frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)[/tex]

Simplify the equation.

[tex]\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)[/tex] [tex]\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)[/tex] [tex]\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )[/tex]

Therefore, this is the 2nd derivative of the function f(x).

We can say that: [tex]f''(x)=36x^2+4[/tex]

Answer 2

Answer:

[tex]y = f(x) = 3 {x}^{4} + 2 {x}^{2} - 8x + 4 \\ \frac{dy}{dx} = 12 {x}^{3} + 4x - 8 \\ \frac{d {}^{2} y}{dx {}^{2} } = 36 {x}^{2} + 4 \\ \boxed{\frac{d {}^{2} y}{dx {}^{2} } = 4(9 {x}^{2} + 1)}[/tex]

f"(x)= 4(9x^2+1)

Related Questions

I NEED URGENT HELP
SOMEONE PLEASE HELP

Answers

Answer:

2x + 3y = -13

Step-by-step explanation:

We can first find the equation of the line in point-slope form. The slope of the line is given by [tex](y_2-y_1)/(x_2-x_1)[/tex], which is (-5-(-3))/(1-(-2)), or -2/3. The equation for a line in point-slope form is [tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line -- in this case, we may use (1, -5). Therefore, the equation for the line is y + 5 = -2/3 (x-1).

The question asks for the equation of the line in standard form -- which is [tex]Ax+By=C[/tex]. We can get this by simplifying the equation above to get[tex]2x+3y=-13[/tex].

What is mZSVT?
Enter your answer in the box.

Answers

Answer:

The measure of ∠SVT is 79°

Step-by-step explanation:

In the given figure

∵ US ∩ RT at V

∴ ∠SVT and ∠UVR are vertically opposite angles

∵ The vertically opposite angles are equal in measures

m∠SVT = m∠UVR

∵ m∠SVT = (5y + 9)°

∵ m∠UVR = (8y - 33)°

→ Equate them

8y - 33 = 5y + 9

→ Add 33 to both sides

∴ 8y - 33 + 33 = 5y + 9 + 33

∴ 8y = 5y + 42

→ Subtract 5y from both sides

∴ 8y - 5y = 5y - 5y + 42

∴ 3y = 42

→ Divide both sides by 3

∵ [tex]\frac{3y}{3}[/tex] = [tex]\frac{42}{3}[/tex]

y = 14

→ Substitute the value of y in the measure of ∠SVT

∵ m∠SVT = 5(14) + 9

∴ m∠SVT = 70 + 9

∴ m∠SVT = 79°

The measure of ∠SVT is 79°

Write 3.0035 as a fraction.
Write the fraction as a mixed number (not an improper fraction). Make sure it is in simplest form.

Answers

The 3.0035 in the mixed number fraction should be [tex]3 \frac{7}{2000}[/tex]

Given that,

The given fraction is 3.0035

Calculation:

[tex]= 3.0035\\\\= 30035 \div 10000\\\\= 6007 \div 2000 \\\\= 3 \frac{7}{2000}[/tex]

Find out more information about the Number here : https://brainly.com/question/17429689?referrer=searchResults

Car Sales A manufacturer of economy cars has determined that 50,000 cars per month can be sold at a price of $18,000 per car. At a price of $17,500, the number of cars sold per month would increase to 55,000. Determine a linear function that predicts the number of cars that will be sold at a price of x dollars. Use this model to predict the number of cars that will be sold at a price of $17,000.

Answers

Answer: 60,000 cars would be sold at $17000.

Step-by-step explanation:

• first we find the slope of the function between two points

(50,000, 18000) and ( 55,000, 17500)

• Let the number of cars sold be the x axis coordinate.

and the price is the y axis coordinate.

• next we plot this points.

m= Change in y / Change in x = rise / run

The slope m = (18000 - 17500/ 50,000 - 55,000)

= -0.1

• The equation of the line in point slope form is m(x-x1)=(y-y1)

• substituting for the first point

-0.1 (X-50,000) = y-18000

-0.1x - 5000 = y - 18000

-0.1x = 18000 + 5000

y = -0.1x + 23000

our slope -0.1 is negative.

In order to find the number of cars to be sold at a price of $17000, substitute this value y in the equation such that:

17000 =-0.1x+23000

solve for x

-0.1x = 23000-17000

0.1x = 6000

divide both sides by 0.1

x = 60000

60,000 cars would be sold at $17,000

A school bus uses 3/4 of a tank to drive back and fourth to school in a week with 5 school days. How much gas does the bus use to drive back and fourth to school in a week with 4 school days?

Answers

Answer:

3/5 of a tank

Step-by-step explanation:

You can use a proportion.

3/4 tank is to 5 days as x is to 4 days

(3/4)/5 = x/4

Cross multiply.

5x = 3/4 * 4

5x = 3

x = 3/5

Answer: 3/5 of a tank

Step-by-step explanation:

17 gallons of gas drive back and fourth

1. Ernie earns $17 per hour tutoring student-athletes at Brooklyn University. a. If Ernie tutored for 12 hours this month, how much money did he earn?​

Answers

Answer:

$17 * 12 hrs = 204

Step-by-step explanation:

A farmer has 12 3/4 acres of land. He wants to divide the land equally among his 5 children. How much land will each child receive?

Answers

Answer:

2.55

Step-by-step explanation:

3/4 is equivalent to 0.75

So,

12 3/4 is equivalent to 12.75

so,

12.75 acres/5 children= 2.55 acres per child

Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x) • g(x).

Answers

Answer:

Simply place the f(x) polynomial over g(x) to get the f(x) / g(x) result. Since polynomials have an infinite domain, the only gap you will get comes from the denominator equaling zero. That happens when:

X - 1 = 0

   +1    +1

   X   = 1

So the domain is: D: X≠ 1

A recipe calls for “18 ounces of cream cheese with 15 ounces of sugar” How many ounces of sugar are there per ounce of cream cheese?

Answers

Answer:

1.2

Step-by-step explanation:

18 divided by 15 equals 1.2

what is 1261/48 so then i could get done with my brain power

Answers

Answer: It is 26.27083333

26.27 if rounded

Suppose you are playing a game of Uno and you must draw two cards from the deck. An Uno deck contains
108 cards. What is the probability that you draw a Skip card or a seven? There are 8 possible chances of
drawing a Skip card and 2 chances of drawing a seven.

Answers

Answer:

hatdog jdudhsisbsn

Step-by-step explanation:

jsysvysbd

Answer:

Explanation:

P(skip or seven) = P(skip) + P(seven)

P(skip) = 8/108
P(seven) = 2/108

P(skip or seven) = 8/108 + 2/108
P(skip or seven) = 10/108 = 5/54

Therefore, the probability of drawing a skip or a seven is 5/54

Using the graph below determine the slopes of the lines in simplest form.

AB = __________
CD = __________
EF = __________
GH = __________

plz help I forgot how to do this

Answers

Answer:AB= -4/3

CD=6/2

EF=Zero

GH=4/6

Step-by-step explanation:

ok  rise/run

I did part A (optional: correct me if i did any wrong on part A). I do not understand part B. Explanation and answer please

Answers

Answer:

   

Step-by-step explanation:

Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help!

Answers

Answer:

Yes because you will still be able to get a Number that will verify.

Step-by-step explanation:

Answer:

You can't predict if they will be less than or greater than either factors because it isn't given if those decimals are positive or negative numbers, and it doesn't state if we should round them.

Step-by-step explanation:

SECTION A
1. The perimeter of a pallalelogram is 38cm. If one of the aide is 12 cm. Find
other side (a) 7cm (b) 9cm (c) 13cm 76
2.​

Answers

Answer:

(a)

Step-by-step explanation:

since a parallelogram has atleast 2 equal sides, we take the 12cm and double it. That equals 24cm. So, 38cm take away 24cm equals 14cm. And since a parallelogram has 4 sides we half 14cm, which gives us 7cm.

When using inverse operations, what should you do to solve x + 7 = 10

Answers

Answer:

10-7=3

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Since we are doing inverse, the opposite of adding is subtracting, so 10-7 is 3.

5
Twenty sixth graders are going on a field trip. They will be
divided into 4 equal groups to take a tour. How many
students will be in each group?

Answers

Answer:

5 students per group

Step-by-step explanation:

20 ÷ 4 = 5 students

Answer:

5

Step-by-step explanation:

20/4=5

A junior high girls' basketball team is to consist of 5 players. How many different teams can the manager select from a roster of 12 girls?

Answers

since each team has 5 players he can make 2 teams
Two teams is the answer

rename 3.5 as a mixed number​

Answers

Answer:

3 1/2

Step-by-step explanation:

.5 equals one half or 1/2

3.5 equals 3 1/2

Answer:

3 ½

Step-by-step explanation:

when you convert your decimal to a mixed number it is the easiest to find a common value of it. if you take ½ and turn it into a decimal it would be .5 or 50/100. its all about finding the lowest common denominator

Helpppppppppppppppppp please......

Answers

Answer:

Ratio of girls to total number of students: 4:12

Step-by-step explanation:

There are four girls, and eight boys.

In all there are 12 students.

So the ratio of girls to total number of students taking swimming lessons is 4:12

I would confirm that it’s 4:12 same answer like on imagine math !

please help me asap​

Answers

Answer:

15/16-3/4 is 3/16. (1/8 simplified)

Step-by-step explanation: Let the 4 turn into a 16. Multiply 4 by 4 to get 16. Then, multiply the numerator by the number you multiplied for the denominator. 3x4 is 12. Now, can subtract. 15-12=3.

Answer:

#5 should be: 0.1875    

and since its different to the ones you have it will be 1 bc the decimal shows as .1

Idk if u want #6 done bc it does not show all answers but i did it anyways :)

#6 should be:−18.16666667

and if there is no decimal points on this one eather it will be -18/16

Step-by-step explanation:

Hopefully this helped, if not HMU and I will try my best to get you a better answer!

Have a great day:)

And if u need help with anything Im here! :)

27% of 140 =
Blank% of 500 = 90
32% of Blank = 8

Help meeeee

Answers

the first one is 10.8 that’s all i know tho sorry

lowest common multiple of 45 and 60​

Answers

Answer:

180

Step-by-step explanation:

why does it have to be 20 character long

What is the answer to 7.13 x 5.5 ?

Answers

Answer:

39.215

that is your answer

The answer will be 39.125

The volume of a cone is 1/3 that of a cylinder when the radius and height are the same (v= 1/3(pi)(r)^2(h). What is the volume of a cone with a radius of 10 inches and a height of 12 inches.

Answers

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Surface Areas and Volumes.

Since, Volume of cone = 1/3 π r^2 h,

here, r = 10 Inches and h= 12 inches, also π =3.14

so, VOC = 1/3 π (10)^2 × (20)

VOC = 1/3(3.14)(100)(20)= 2093.33 inch^3

=> so the volume of the cone is 2093.33 cubic inches.

How many decimal places are in the product of 1.91 and 2.3? one two three four​

Answers

Three! Because there is a total of 3 numbers after both 1.91 and 2.3.

Hope I helped!

Answer:

C.3

Step-by-step explanation!

because there is a total of 3 numbers after both 1.91 and 2.3.

Hope this helps you!

MARK BRAINLIEST!!!!!!! At a display booth at an amusement park, every visitor gets a gift bag. Some of the bags have items in them as shown in the table below. Items in the Gift Bags Items Bags Hat Every 2nd visitor T-shirt Every 7th visitor Backpack Every 10th visitor How often will a bag contain all three items? LCM or GCF?

Answers

Answer:

Step-by-step explanation:

you would find the least common multiple. If you have a set number of gift bags, and you want to find how many had all 3 at once, you would find the LCM that fit within the number of gift bags that you had in order to find it. in this case, it would be 1 in 70

It cost Benjamin $1.35 to send 9 text messages how much would it cost to send 118 text messages

Answers

Answer:

it costs $17.7

Step-by-step explanation:

1.35/9 is 0.15

0.15 * 118 = 17.7

need answer ASAP pls

Which is the independent variable in the graph of the U.S. population 1800-1900?

United States
straight lines
years
population

Answers

Answer: United States

Step-by-step explanation: Because threats the only independent variable the rest are dependent on others.


Please please help me

Answers

Answer:

the answer is c. it’s commutative property

Step-by-step explanation:

12-(y•2) is the same as 12-(2•y) 2 and y are just flipped around. hope this helps!

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