Given the function f ( x ) = − 1 x + 3 x 4 , f(x)=− x 1 ​ + 4 3 x ​ ​ , find f ′ ( 4 ) . f ′ (4). Express your answer as a single fraction in simplest form.

Answers

Answer 1

Step-by-step explanation:

The question is not well written. Let us say the function given as expressed as;

f(x) = -1/x + 3/x⁴

f'(x) means we are to differentiate the function with respect to x;

Given f(x) = axⁿ

f'(x) = naxⁿ⁻¹

f(x) = -x⁻¹ + 3x⁻⁴

Applying the differentiation formula we will have;

f'(x) = -1(-x⁻²)+(-4)3x⁻⁴⁻¹

f'(x) = x⁻²-12x⁻⁵

Express as a fraction

f'(x) = 1/x²-12/x⁵

To get f'(4), we will have to substitute x = 4 into the resulting expression

f'(4) = 1/4²-12/4(5)

f'(4) = 1/16-12/20

f'(4) = 1/16-3/5

Find the LCM

f'(4) = (5-48)/80

f'(4) = -43/80

Note that the function used was assumed but the same method can be employed to any other functions.


Related Questions

y + 2x = −1
3y − x = 4

Answers

Answer:

Step-by-step explanation:

Let's solve for x.

y+2x=−1

Step 1: Add -y to both sides.

2x+y+−y=−1+−y

2x=−y−1

Step 2: Divide both sides by 2.

2x

2

=

−y−1

2

x=

−1

2

y+

−1

2

Answer:

x=

−1

2

y+

−1

2

Answer:

Answers below

Step-by-step explanation:

Q1.  2x=−1−y

=

​2

​−1−y

​​

Q2.     −x=4−3y

x=−4+3y

x=3y−4

Karina is showing her steps to solve the expression −26.7 ÷ one third. (1 point) In which step did Karina make an error? Step 1: −26.7 ÷one third Step 2: −26.7 ⋅ −3 Step 3: 80.1

Answers

Answer:

step 2

Step-by-step explanation:

step 2 is supposed to be (-26.7 multiply by 3) since the reciprocal of 1/3 is 3 and not -3. the answer should be -80.1 instead of 80.1

Tom had 54 songs on his MP3 player. If he deleted 9 songs, what is the ratio of songs he kept to songs he deleted?

Answers

Answer:

6:1

is the right answer

Step-by-step explanation:

Answer:

45:9 or 49 to 9

Step-by-step explanation:

If you subtract 54-9 because the question is asking what is the the ration from what he KEPT after he deleted 9 so you would subtract so the answer wouls be 45:9 or 49 to 9

12. DEDUCE The graph of a linear
equation is in the form y = mx + b.
Are there any values of m that would
result in the graph not representing
a function? Explain your ans
answer.
Please help it’s due today I will mark you brainless

Answers

Answer:

en contexto, ora al de arriba pa que te ayude porque nose nada xd

Step-by-step explanation:


Write 3 quadratic equations that are NOT
equivalent, each forming a graph with vertex (-2, 3)

Answers

Answer:

the vertex of a quadratic equation:

a*x^2 + b*x + c = y

Is located at:

x = -b/2a.

In this case, x = -2

Then:

-b/2a = -2.

And we also have that:

a*(-2)^2 + b*-2 + c  = 3

Then we have two equations:

-b/2a = -2

a*(-2)^2 + b*-2 + c  = 3

We have only 2 equations and 3 variables, so we can just give the variable c different values and we will find different quadratic equations that are not equivalent.

Let's begin with c = 0, our equations are:

-b/2a = -2

a*(-2)^2 + b*-2 + 0  = 3

In the first equation we can isolate b and get:

b = 4*a

Now we can replace this in the other equation and solve this for a.

a*4 + 4*a*-2 = 3

-4*a = 3

a = -3/4

then:

b = 4*a = 4*-3/4 = -3

The first quadratic equation is:

(-3/4)*x^2  - 3*x = y.

Now, to find the second let's use a different value of c.

c = 1

b = 4*a

a*(-2)^2 + b*-2 + 1  = 3

Let's solve in the same way as before:

a*4 + (4*a)*-2 + 1 = 3

-4*a = 2

a = 2/-4 = -1/2

b = 4*-1/2 = -2.

Then our equation is:

(-1/2)*x^2 - 2*x + 1 = y

For the last equation, let's use c = 2.

then our equations are:

b = 4*a

a*(-2)^2 + b*-2 + 2  = 3

Same as before, replace the first equation in the second.

a*4 + (4*a)*-2 + 2 = 3

-4*a + 2 = 3

-4*a = 1

a = -1/4

Then:

b = 4*(-1/4) = -1

Our third equation is:

(-1/4)*x^2 - 1*x + 2 = y

Now, below you can see all of them graphed.

Where red is the first one, blue the second and green the third one. (and as you can see, all of them share the vertex (-2,3) )

Jennifer has already driven 160 miles on her trip to her grandparents house for every hour she travels she drives an additional 55 miles which equation represents the relationship between the Total miles driven y,and the number of hours ,x.

Answers

Answer:

y = 55x + 160

Step-by-step explanation:

The computation of the equation that represents the relationship between the total miles driven y and the number of hours x is shown below:

she starts at 160 miles so it would be y-intercept

So the equation form would be

"b" in y = mx + b

where,

m = 55

and b = 160

Therefore the equation would be

y = 55x + 160

The same is to be considered

The figures below are similar. Find the length of the missing side.
14
10
56
40
14
х
56

Answers

Answer:

12

Step-by-step explanation:

Everything is multiplied by 4

I am not sure and I’m sorry if I get this wrong but I think it’s 12....

what is the answer to 805÷24 plz tell me

Answers

Answer:

33.5416666667

Step-by-step explanation:

805/24 math problems division = 33.5416666667. Therefore 33.5416666667 to 2 decimal places= 33.54

805/24 divided by 2 » (805/24) ÷ 2 » 33.5416666667 ÷ 2 = 16.7708333333 . Check 805/24 long division below

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.

Solve by factoring.

x^2 + 6x = -9. Hint: This is a double root.

Answers

Answer:

x=-3

Step-by-step explanation:

my work is in the picture. lmk if you need me to explain more

Conocido popularmente como el Lanzón, es una escultura elaborada por la cultura Chavín de Perú. Este gran monolito data, aproximadamente, del año 1000 a. C. y está situado en el Viejo Templo del centro religioso y ceremonial de Huantar.

Cierto día en una visita cultural, Pedro decide representar el Lanzón Monolítico con una escala de 1:103 cuya medida es de 4,41 cm.
Teniendo en cuenta los datos de la situación. ¿Cuánto mide la altura real exacta del Lanzón en metros?

Answers

Answer:

La altura real del Lanzón Monolítico es de 453.23 centímetros, o 4.53 metros.

Step-by-step explanation:

Dado que la representación a escala del Lanzón Monolítico mide 4,41 centímetros, y que dicha escala tiene un valor de 1:103 respecto de la medida real de la escultura, para representar la altura real de la misma se requiere realizar el siguiente cálculo:

1 = 4,41

103 = X

(103 x 4,41) / 1 = X

454.23 = X

Por lo tanto, la altura real del Lanzón Monolítico es de 453.23 centímetros, o 4.53 metros.

Consider that x = 5 and y = 7. Which statement is true about x + y? A) The sum of x and y is a rational number. B) The sum of x and y is an imaginary number. C) The sum of x and y is an irrational number. D) The sum of x and y is neither rational nor irrational. ​

Answers

Answer:

The answer is 12

Step-by-step explanation:

because 7 plus 5 is 12

Find the remaining zeros of f using the given information about the polynomial.

Then write the linear factorization of the polynomial. Degree 4;
zeros: 3i, square root {7}

Answers

Answer:

noloce necesito puntos

told u aint doing my work help

Answers

Answer:

A: 50:100

Step-by-step explanation:

The ratio 5:10 is the ratio of caramels to fruit creams.  This ratio is equivalent to 50:100.

Can somebody plz answer all of them correct! (Only if u done this before)
thanks! WILL MARK BRAINLIEST
(Don’t judge me..I didn’t study so I need to do corrections)

Answers

Answer:

23) 53/100

24)2/5

25)3/5

26)11/50

27)17/50

28)19/1000

29)4/5

30)1/250

31)9/25

32)1 3/10

33)11 1/2

34) 7 3/40

Step-by-step explanation: Hope this helps!

What transformation moves Frame 1 to Frame 2?
A) Translation
B) Rotation
C) Reflection
D) Dilation

Answers

Translation is the answers

The birth weights of newborn babies in the United States follow a normal distribution with a mean of 3.4 kg and a standard deviation of 0.6 kg. Researchers interested in studying how children gain weight decide to take random samples of 100 newborn babies and calculate the sample mean birth weight for each sample. Calculate the mean and standard deviation of the sampling distribution

Answers

Answer:

3.4 kg

0.06 kg

Step-by-step explanation:

Given that:

Birthweight follows a normal distribution :

Mean weighf (m) = 3.4 kg

Standard deviation (σ) = 0.6 kg

Sample size (n) = 100 new born babies

calculate the sample mean birth weight for each sample. Calculate the mean and standard deviation of the sampling distribution

The sample mean birth weight = population mean birth weight for a normal distribution according to the central Limit theorem.

Hence, sample mean birth weight = 3.4kg

Standard deviation of sampling distribution = standard error = σ/√n

0.6 / √100

= 0.6 / 10

= 0.06 kg

Using the Central Limit Theorem, it is found that:

The mean is of 3.4 kg.The standard deviation is of 0.06 kg.

Central Limit Theorem The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem:

Mean of 3.4 kg, hence [tex]\mu = 3.4[/tex].Standard deviation of 0.6 kg, hence [tex]\sigma = 0.6[/tex].Samples of 100, hence [tex]n = 100, s = \frac{0.6}{\sqrt{100}} = 0.06[/tex]

Hence, the mean of the sampling distribution is of 3.4 kg and the standard deviation is of 0.06 kg.

To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/24663213

Yul has lunch at a restaurant. If his bill was $14.50 and Yul wants to leave a 20% tip, what is the amount he should leave for the tip? What is the total amount for his meal plus tip?

Answers

Answer:

Yul has lunch at a restaurant. If his bill was $14.50 and Yul wants to leave a 20% tip, what is the amount he should leave for the tip?

 

Yul should leave 20% tip of

 

14.50 * 0.20 = 2.9

Pencils cost 25 cents apiece. Rulers cost 80 cents
apiece. Susan spent $20 for a total of 36 rulers and
pencils. How many pencils did she buy?

Answers

Answer:

She bought 16 pencils

Peter is planting trees in his yard. He wants the ratio of pine trees to oak trees to be 3 to 2. Peter wants to plant a total of 45 trees. How many pine trees should he plant?

Answers

Answer:

Step-by-step explanation:

Let the ratio of pine tree to oak tree=3x:2x

Where no. Of pine tree =3x

No. Of oak tree=2x

Total no. Of tree = 3x+2x=45

5x=45

X=9

So no. Of pine tree=3x=3x9=27 tree is answer

The equations of four lines are given. Identify which lines are parallel.
Line 1: y= 2 - 6
Line 2: 3 - 2y = -1
Line 3: y = 4x + 6
Line 4: y+3= 1 (2-6)

Answers

Answer:

lines 1 and 4

Step-by-step explanation:

they are both horizontal lines because when solved equal a number without an x so they is no slope so they are horizontal and have the same slope which means they are parallel to each other

I’m in a test pls help
Use inductive reasoning to write the next two terms in each sequence of numbers.

B.) 720, 180, 360, 90, _____, _____ .

Answers

Answer: 180, 45

Step-by-step explanation:

First, you look at the patterns for each numbers, so you can apply the rules for the next two sequences

720 divided by 180 = 4

360 divided by 180 = 2

360 divided by 90 = 4

for the next sequences, you multiply the last number by 2 (90 x 2 =180)

then divide the answer by 4 to get the answer (180 divided by 4 = 45)

so the next two numbers are 180, 45

Mark me as the brainiest answer

. f(-5) = 5, f (0) = 10

Answers

Answer:

On the screenshot (y=x+10)

Step-by-step explanation:

Have a great day!

BRAINLY FOR RIGHT ANSWER AND STEP BY STEP LOTS OF POINTS BTW
A car’s fuel economy E(miles per gallon) is given by the formula E=mg, where m is the number of miles driven and g is the number of gallons of fuel used.
Solve the formula for m.
If Sally’s car has an average fuel consumption of 30 miles per gallon and she used 9.5 gallons, how far did she drive?

Answers

Answer:

60 miles

Step-by-step explanation:

What is the area of this figure

Answers

Insert a picture so I can help you out :)
Let me see te picture.Area= length x width

A regular dodecagon (12 sided polygon) is rotated n degrees about it's center, carrying the dodecagon onto itself. What is the minimum number of degrees it must be rotated to carry the dodecagon onto itself? *
A. 30 degrees
B. 15 degrees
C. 60 degrees
D. 90 degrees
Which one?

Answers

Answer:

30 degrees

Step-by-step explanation:

Use inductive reasoning to predict the next line in this sequence of computations. Then use


a calculator or perform the arithmetic by hand to determine whether your conjecture is


correct.


9.3+5 = 32


99.3 + 5 = 302


999. 3+5 = 3002


9999.3+5 = 30002


Make a conjecture by predicting the correct numbers in the line below.


0-3+5 -0


Is the conjecture correct?


O A. Yes


OB. No

Answers

Answer and explanation:

Inductive reasoning is a method of reasoning whereby conclusion of an argument is based on specific observations or evidence that forms the premise of the argument. Inductive reasoning moves from observations to general conclusion unlike deductive reasoning.

B. The conjecture 0-3+5 -0 is incorrect

Given the above sequence of computations, we use inductive reasoning to predict the next computation

The correct next conjecture is

99999.3+5= 300002

-(-2-n) simplify please

Answers

Answer:

2 - n

Step-by-step explanation:

Subtract a negative is the same thing as adding a positive, so -(-2 - n) is the same thing as 2 - nWhat we did there was cancel out the two minus signs, and formed a positive.

I hope this helps!

I NEED THE ANSWER NOW

Answers

1/8 is the answer to the question
1/8 is the correct answer

A line has the equation y = 1/3x - 5 . Find the equation of a parallel line passing through the point (3, 2).

Answers

Answer: y=1/3x+1

Y needs to be changed in order to maintain parallelism.

Good Luck!

Answer:

The answer is y=1/3x+1

Step-by-step explanation:

y=mx+b

m=1/3

y-y=m(x-x1)

y-2=1/3(x-3)

y-2= 1/3x-1

+2 +2

y=1/3x+1

What is the equation in slope intercept form of the line that passes through the points (-4, 47) and (2, -16)?

Answers

Answer:

slope intercept form- y= -21/2x +5

Point slope form= y-47=-21/2 (x+4)

Step-by-step explanation:

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