Using the alternate form of the definition of the derivative, Compute f'(c) for f(x) = x+4/x, c=4

Answers

Answer 1

The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.

What is the value of the derivative of a function?

In this problem we have the following rational equation, which is equivalent to the following sum of functions:

f(x) = (x + 4) / x = 1 + 4 / x = g(x) + h(x)

Then, we must find both the derivatives of the functions g(x) and h(x) by using the definition of derivative:

g(x):

g'(x) = [1 - 1] / h

g'(x) = 0 / h

g'(x) = 0

h(x):

h'(x) = [4 / (x + h) - 4 / x] / h

h'(x) = [4 · x - 4 · (x + h)] / [h · (x + h) · x]

h'(x) = - 4 · h / [h · (x + h) · x]

h'(x) = - 4 /[(x + h) · x]

If h = 0, then:

h'(x) = - 4 / x²

Then, the first derivative of the function is f(x) = - 4 / x². Now we evaluate the function at x = 4:

f(4) = - 4 / 4²

f(4) = - 1 / 4

The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.

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Related Questions

Roy has $253.97 in his bank account. He loans his friend $81.19. How much money does he have in his
account?

Answers

Answer:

172.78

Step-by-step explanation:

Can anyone please help me with #3 ASAP I’ll mark you brainly

Answers

Check out the attached photo

Solve the calculation

Answers

Answer:

83° 59'

Step-by-step explanation:

The numbers given refer to degrees and minutes for two angles

We read them as follows

62° 18'   ==> 62 degrees and 18 minutes

21° 14'    ==>  21 degrees and 41 minutes

60 minutes make up 1 degree

We simply add the individual components together. If the number of minutes is 60 or greater then we have to convert those minutes to degree and minutes and add to the total degrees

In this case it is a simple addition since 18' + 41' = 59' and is less than 60

So 62° 18' + 21° 14'  

==> Add the degrees separately ==> 62 + 21 = 83°

==> Add the minutes separately ==> 18' + 41' = 59'

Put the two components together to get

83° 59'

83° 59'
Answer is 83° 59'

Solve the formula for the specified variable.
I = Prt
t

Answers

The answer is T=I/pr

graph both lines on the same coordinate plane y=1/3x+3 and y+1=3x
how do i graph this?

Answers

Answer:

Step-by-step explanation:

you need to turn the second y equation into the correct format, so it needs to be y=. Subtract the 1 from the left side and but it on the right side. Your equation should y=3x-1. To graph this on paper, you would go 1 down on the y axis, then rise (go up) 3 and run ( go over) one.on a calculator plug it into the y1 function and y2 function and then press graph.

5. This diagram is a straightedge and
compass construction. Which triangle is
equilateral? Explain how you know.

Answers

The ΔVZW is Equilateral Triangle .

Equilateral Triangle is defined as the triangle in which all the three sides of the triangle are equal.

For Example ; if a triangle ABC has lengths AB=2cm , BC=2cm and CA=2cm    then the triangle ABC can be called as an equilateral triangle as all sides have same length i.e. 2cm .

In the question ,

From the diagram, we have the radius of all the circles are of equal length ,

Since the radius of all the circles are equal in length , their diameter will also be equal in length .

We can see from the diagram that VZ , ZW and WV are the diameters of the circles , So they will be equal in length ,

which means VZ = ZW = WV.

In triangle VZW the sides VZ , ZW and WV  are of equal length , hence the triangle will be an Equilateral Triangle.

Therefore , the Triangle VZW is Equilateral Triangle .

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Write the improper fraction 30/7 as a mixed number

Answers

Answer:

Step-by-step explanation:

30/7 = 4 2/7

Because 7 only goes into 30, four times (7 x 4 = 28) anything else would be too big.

7 goes into 30 four times, and you get left with a remainder of 2

So you write 4 wholes, then 2/7 because 2 is the remainder it goes on top, and 7 stays in the denominator (bottom)

If y= 50 degrees and z=85 degrees, then x in degree is=?
the answer will be 55 degrees. please solve

Answers

Answer:

Step-by-step explanation:

Question 2 of 10
Solve x + 4 = 6.
OA. x = -2 and x = 10
OB. x 2 and x = -10
OC. x = -2 and x = -10
OD. = 2 and x = -2

Answers

The solution for x in the equation is x  = 2

What are linear equations?

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

How to determine the solution of the equation?

The equation is given as

x + 4 = 6

Subtract 4 from both sides of the equation

So, we have

x + 4 - 4 = 6 - 4

Evaluate the like terms

So, we have

x  = 2

Hence, the solution for x in the equation is x  = 2

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What’s the answer?
5x + 12(19 - x) = 19(1678)

Answers

your answer should be x=-4522

Watch help video
Given g(x) = 2x + 3, find g(0).

Answers

Answer:

g(0) = 3

Step-by-step explanation:

Hello!

Substitute 0 for x in the equation.

Evaluateg(x) = 2x + 3g(0) = 2(0) + 3g(0) = 0 + 3g(0) = 3

g(0) is 3.

what is the nth term of 1, 3, 9

Answers

Answer:

3ⁿ

Step-by-step explanation:

The nth term is:

3ⁿ

Learn
Look at this equation:
C
c³ = 125
What is c, the cube root of 125?

Answers

C = 5.

5^3 = 5 x 5 x 5 = 125.

I hope this helps!!

A university wants to know more about the knowledge of students regarding international events. They are concerned that their students are uninformed regarding news from other countries. A standardized test is used to assess students’ knowledge of world events (national reported mean= 65, S = 5). A sample of 30 students is tested (sample mean=58, Standard Error=3.2). Compute a 99 % confidence interval based on this sample data. How do these students compare to the national sample?

Answers

A university wants to know more about the knowledge of students regarding international events. They are concerned that their students are uninformed regarding news from other countries. A standardized test is used to assess students’ knowledge of world events (national reported mean= 65, S = 5). A sample of 30 students is tested (sample mean=58, Standard Error=3.2). Compute a 99 % confidence interval based on this sample data. How do these students compare to the national sampl

:Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle and the other moving at constant velocity with respect to the particle. This postulate is known as the law of inertia.

Use the domain {1/2, 1, 2, 4, 8, 16} and plot the points on the graph that would best satisfy the equation y = log2x.

Answers

Given equation  y = log2x

         domain {1/2, 1, 2, 4, 8, 16}.

The graph of six points that would satisfy the equation.

 In equation put the value of

x =1/2

y= -1

for x= 1

     y=0

for x= 2

    y=1

for x= 4

     y=2

for x =8

    y= 3

for x= 16

    y=4

Plot the points  {1/2, 1, 2, 4, 8, 16}  on a coordinate plane

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what is the answer ???

Answers

Answer is 11/14 (the last choice)

Step by step

She reads 5 1/2 novels per week
We know a week is 7 days

Divide 5 1/2 by 7

Change both numbers to improper fractions

11/2 divided by 7/1

When dividing fractions you flip the divisor and multiply

11/2 x 1/7

Multiply across 11 x 1 and 2 x 7

11/14 is your answer

Problem solved!

There are 9 lions there are fewer cubs than lions how many fewer cubs are there ?

Answers

Number of cubs are less than 9.

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

NO. OF LIONS = 9

Cubs are fewer than 9

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4(x+5)-2x/3 when x=6

Answers

Plug 6 into the problem
1) 4((6)+5)-2(6)/3
Add 6 + 5 to get 11
Multiple 2 • 6 to get 12. But remember that there is a negative sign before it so it would be negative.

2) 4(11)-12/3
Multiply 4 • 11 to get 44
Divide -12/3 to get -4

3) 44-4
Subtract

4) 40

Write an expression to represent: 9 more than the quotient of 2 and x

Answers

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is [tex]\frac{2}{x}[/tex].

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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A=bh;A=5,h=5
HELP ME

Answers

Answer:

b = 1

Step-by-step explanation:

5 = 5b

b = 1

Enter your answer as a proper fraction, or mixed number.

Answers

Answer:

3/14

Step-by-step explanation:

Answer:

3/14

Step-by-step explanation:

(a) Use the iteration formula +1=10-2x, to find the values of X₁, X2 and xs
Start with Xo = 2

Answers

The value for the given question is x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.

Given iteration formula as xₙ ₊ ₁ = ∛ 10 - 2xₙ

Given x₀ = 2

We have to find the values of x₁, x₂, and x₃ as

For finding the value of x₁ we need to substitute n = 0 as

xₙ ₊ ₁ = ∛ 10 - 2xₙ

x₀ ₊ ₁ = ∛ 10 - 2x₀

x₁ = ∛ 10 - 2(2)    (∵ x₀ = 2)

x₁ = ∛ 10 - 4

x₁ = ∛ 6

x₁ = 1.8

For finding the value of x₂ we need to substitute n = 1 as

xₙ ₊ ₁ = ∛ 10 - 2xₙ

x₁ ₊ ₁ = ∛ 10 - 2x₁

x₂ = ∛ 10 - 2(1.8)    (∵ x₁ = 1.8)

x₂ = ∛ 10 - 3.6

x₂ = ∛ 6.4

x₂ = 1.85

For finding the value of x₃ we need to substitute n = 2 as

x₂ ₊ ₁ = ∛ 10 - 2xₙ

x₂ ₊ ₁ = ∛ 10 - 2x₂

x₃ = ∛ 10 - 2(1.85)    (∵ x₀ = 1.85)

x₃ = ∛ 10 - 3.7

x₃ = ∛ 6.3

x₃ = 1.846

Therefore, the value of x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.

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If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=0, what is the exact measure of θ?

Answers

Step-by-step explanation:

y of o but you dont have to use y

A local company has K2,500 to set up an annuity to be paid quarterly for 5 years. The payments of that annuity are to be increased in line with the current interest rate. The account pays interest at 10% p.a. compounded quarterly,

a) Calculate the size of each payment during the first year.

b) What is the size of the final payment (payment at the end)?​

Answers

Answer:

Step-by-step explanation:

(a).

Within 1 year, there would be 4 payments to be made.

therefore, PMT= [tex]\frac{P(1+i)}{n} = \frac{2500(1+0.025)}{4*5} =\frac{2562.5}{20} = $128.125[/tex]

(i) 1st payment will be :PMT $128.125

(ii) 2nd payment will be :128.125*(1.025)^1= $131.33

(iii) 3rd payment will be :128.125*(1.025)^2=$134.61

(iv) 4th payment will be :128.125*(1.025)^3=$137.98

Hence the payments are: $128.125, $131.33, $134.61, and $137.98.

(b).

The size of the final payment [tex]PMT(1+i)^{m-1}[/tex] where m 4 *5= 20

[tex]=128.125(1+0.025)^{20-1} \\=128.125(1.025)^{19} \\=$204.83[/tex]

13/2^2-10(13/2)+23 find the answer just evaluate

Answers

Answer:

Step-by-step explanation:

-38 3/4

The total payroll for a baseball team is 2.48 × 109 dollars, and the total payroll for a football team is 2.8 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?

0.32 × 109 dollars
2.7752 × 109 dollars
2.7752 × 1011 dollars
3.2 × 1011 dollars

Answers

Answer: its c

Step-by-step explanation:

The difference between the payroll of football and baseball is 2.7752 × 10¹¹. Hence, option C is correct.

What is an equation?

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine the value of an unknown variable that represents an unknown quantity.

The payroll of the baseball team is 2.48 × 10⁹ and,

The payroll of the football team is 2.8 × 10¹¹.

So, the football team's payroll is more than the baseball team's payroll by,

(2.8 × 10¹¹) - (2.48 × 10⁹)

= 2.7752 × 10¹¹.

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How do I solve this absolute value in quality problem

|2t + 2/3|≤4

Answers

Answer: -7/3≤t≤5/3

Step-by-step explanation:

|2t + 2/3|≤4

2t + 2/3≤4

(2t + 2/3≤4)*3

6t+2≤12

6t≤10

t≤10/6

t≤5/3

2t + 2/3>=-4

(2t + 2/3>=-4)*3

6t + 2>=-12

6t>=-14

t>=-14/6

t>=-7/3

-7/3≤t≤5/3

To hire an accountant to prepare taxes costs a flat fee and an additional hourly rate. The amount the accountant costs can be modeled by the function A(x)= 150+35x, where x represents
the number of hours the accountant works to prepare the taxes and 150 represents the flat fee. What is the value of A(220) and its interpretation?
A. A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
B. A(220)=7850; If the accountant takes 7,850 hours to prepare the taxes, the cost will be $220.
C. A(220) = 2; If the accountant takes 220 hours to prepare the taxes, the cost will be $2.
D. A(220)=2; If the account takes 2 hours to prepare the taxes, the cost will be $220.

Answers

D is the answer because i you have to decide 220 by 2

Answer:

A. A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.

Step-by-step explanation:

what is the amount of elements in each region

Answers

From the given Venn Diagram, the number of elements in each region is given by:

I = 9.II = 3.III = 6.IV: 4.V: 8VI = 7.VII = 5.VIII = 2.

How to find the number of elements in each region of the Venn Diagram?

We start from the most restricted region, and count the other regions.

From the intersection of A and C, we have that:

IV + V = 12.

IV + 8 = 12.

IV = 4.

From the intersection of B and C, we have that:

VI + 8 = 15.

VI = 7.

From the intersection of A and B, we have that:

II + V = 11.

II + 8 = 11.

II = 3.

From set A, we have that:

I + II + IV + V = 24.

I + 3 + 4 + 8 = 24

I = 9.

From set B, we have that:

II + III + V + VI = 24.

3 + III + 8 + 7 = 24.

III = 6.

From set C, we have that:

IV + V + VI + VII = 24.

4 + 8 + 7 + VII = 24.

VII = 5.

From the universe set, we have that:

I + II + III + IV + V + VI + VII  + VIII = 44.

9 + 3 + 6 + 4 + 8 + 7 + 5 + VIII = 44.

VIII = 2.

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What is -12 + 12 x 10?

Answers

108

Explanation

- 12 + 12 • 10

- 12 + 120

108

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