Show that f '(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f − g is constant? If f '(x) = g'(x) for all x in an interval (a, b), then f − g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant.

Answers

Answer 1

Answer:

Answer: 15 cm

Step-by-step explanation:

Answer 2

The derivative of a function at a point can be defined as its slope at that point. For f'(x) = g'(x) in the interval (a,b), it is proved that f - g is constant in (a,b).

What is a Derivative?

A derivative of a function is its rate change of increase or decrease in a given interval with respect to its variable. Derivative of a constant function is always zero.

Given that, f'(x) = g'(x) for all x.

Taking integral on both sides

f(x) + C₁ = g(x) + C₂

=> f(x) - g(x) = C₂ - C₁

=> f(x) - g(x) = C

Thus, f(x) - g(x) is constant is proved.

Similarly for interval an interval (a,b),

f(x) - g(x) = C

=> f(x)= g(x) + C

Hence, it is proved that in an interval (a,b), if  f'(x) = g'(x) then f(x)= g(x) + C.

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Related Questions

HIT THE QUANNN AY HIT THE QUANN I SAY GET DOWN LOW AND SPREAD YA ARMS

Answers

Answer:

ok

Step-by-step explanation:

Jim has 3 pairs of pants
and 2 shirts. How many
different ways can he
dress?

Answers

Answer:

2 to 5 different ways

Step-by-step explanation:

Answer:

12 different ways he can dress

Step-by-step explanation:

Let The Pant be A and Shirt be B

So, we have 3 pair of pants i.e., 6 Pants

Here, We assumed that the pant be A then 6 pants be

A₁ A₂ A₃ A₄ A₅ A₆

Now, For Shirts

We have 2 Shirts

But we assumed that the Shirt be B then 2 Shirts be

B₁ B₂

Then, We will make pair of A and B

A₁ = B₁

A₂ = B₁

A₃ = B₁

A₄ = B₁

A₅ = B₁

A₆ = B₁

A₁ = B₂

A₂ = B₂

A₃ = B₂

A₄ = B₂

A₅ = B₂

A₆ = B₂

Thus, 12 different ways he can dress

-TheUnknownScientist

how many solutions does the system have 6x+3y=-12 y=-2x+4

Answers

Answer: No solutions

Step-by-step explanation: These equations, when done by substitution, end up not equaling each other.

the ratio of boys and girls in class is 3:2 Tthere are 15 boys how many total of boys and girls are in class

Answers

Answer: 15 boys and 10 girls

Step-by-step explanation:

15/3=5, so the you have to multiply 2 by 5 to get the number of girls. 2x5=10, so to get the total number of students you add 15+10 which gets you 25 students, but if it’s just asking for girls, then it’s 10.

Answer:

25

Step-by-step explanation:

3:2 = 15:10 ( 3x5 = 15 boys; 2x5 = 10 girls)

15+10=25 total boys and girls

Determine whether the lines are parallel, perpendicular, or neither. Justify your answer. y = 2x - 8
Y = 1/2x + 6
⚠️if you answer correctly I will give you brainlyest⚠️

Answers

Answer:

They are parallel, they will never intersect.

Step-by-step explanation:

Notice that they have exactly the same steepness, which means their slopes are identical. The only difference between the two lines is the y-intercept. If we shifted one line vertically toward the y-intercept of the other, they would become the same line.

x/2 + 6

This is the simplest form because you can’t combine x with 6.

Rewrite 14 1/3 as an improper fraction

Answers

Answer:

Step-by-step explanation:

((14×3) + 1 )/3 = (43/3)

14 1/3 can be expressed as 43/3, which is an improper fraction.

To rewrite 14 1/3 as an improper fraction, we need to convert the mixed number into a fraction.

First, we multiply the whole number (14) by the denominator of the fraction (3) and add the numerator (1). This gives us the numerator of the improper fraction. The denominator remains the same.

14 × 3 = 42

Next, we add the numerator (1) to the result we obtained above.

42 + 1 = 43

Therefore, the improper fraction equivalent to 14 1/3 is 43/3.

In the fraction 43/3, the numerator (43) represents the total number of parts we have, and the denominator (3) represents the size of each part. It indicates that we have 43 equal parts of size 1/3.

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Which situation has a net result of zero?
The temperature was -9'F and fell 9°F.
Janet had $4 and gave $3 to her friend.
High tide was 5.5 ft and now low tide is -0.5 ft.
The hot-air balloon rose 539 feet. It then lost 539 feet of altitude.

Answers

Answer:

D. The hot-air balloon... results in a net of zero

Step-by-step explanation:

Thanks for the points my guy :)

have a great day

Answer:

canberry

Step-by-step explanation:

Which area on the map is home to the most petroleum fields in Europe?


A) A

B) B

C) C

D) D

Answers

Answer: I think the answer is D

Step-by-step explanation:

Which expression is equivalent to 5(2y + 8) − 4y ?



A. 6y + 40


B. 6y + 8


C. 14y + 40


D. 14y + 8

CMON PLEASE ITS TIMED.

Answers

Answer:

I also think its A.

Step-by-step explanation:

10y + 40- 4y

(10y-4y)+40

6y+40

How many different ID cards can be made if there are six digits on a card and no digit can be used more than once?

Answers

Answer:

10

Step-by-step explanation:

I share wwe smackdown ​

Answers

Answer:

Ok..

Step-by-step explanation:

Answer:

It’s fake

Step-by-step explanation:

Graham decided to play football this year instead of getting a part-time job. Last year he made about $1,100 during football season. He also spends about $9 on eating out after each game. His team plays a 10-game season. What is his opportunity cost of playing football?

Answers

10,091 because it's a 10 season football season and he spends 9 dollars every game

Step-by-step explanation:

ez

The opportunity cost of playing football for Graham is $1,190.

What is the Opportunity cost?

The opportunity cost of certain activity in microeconomic theory is the value or gain given up by engaging in that activity in comparison to engaging in an alternative activity. Simply put, if you do a bone activity, you forfeit the potential to choose another.

Given that Graham made $1,100 during football season. Also, Graham spends about $9 on eating out after each game and his team plays a total of 10 games in a season.

Therefore, the opportunity cost of playing football for Graham is,

Opportunity cost

= Amount that Graham would have made in a part-time job +  Total cost of playing football season

= $1,100 + (Number of games × Amount spend in a single game)

= $1,100 + (10×$9)

= $1,100 + $90

= $1,190

Hence, the opportunity cost of playing football for Graham is $1,190.

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Which linear function has the same y-intercept as the one that is represented by the graph?
Oy=2x-4
Oy=2x-3.
Oy=2x+3
Oy=2x+4

Answers

Answer:

Oy=2x+3

Step-by-step explanation:

The function that has the {y} - intercept as that of the function graphed is y = 2x + 3

What is function?

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to find the linear function that has the same y-intercept as the one that is represented by the graph.

The function graphed has the {y} - intercept of 3.

For the functions given -

Functions              {y} - intercept

y=2x-4                        -4

y=2x-3.                       -3

y=2x+3                        3

y=2x+4                        4

So, the function that has the {y} - intercept of 3 is y = 2x + 3.

Therefore, the function that has the {y} - intercept as that of the function graphed is y = 2x + 3.

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Find the distance between a and b

Answers

Answer:I believe it is 2.4

Step-by-step explanation:

Question 1 Imaginary & Complex Numbers-Addition & Subtraction Solve the following: (7 – 21) – (2+61) = O 9 +82 O 5 - 42 0 5 - 82 0 5+ 8i​

Answers

Answer:this did not work for me

Step-by-step explanation:

Put -4.8, -4/1 10, and -17/4 in order from LEAST TO GREATEST

Answers

I think it’s -4/1 10, -4.8, -17/4 , 10 if ten wasn’t apart of -4/1 10 sorry if it’s not :/

2= f/8 f= solve the equation

Answers

2= f/8
F is being divided by eight , when moving across equal sign the sign is opposite.
2 x 8 = f
16=f

This question is designed to be answered without a calculator.

Use this graph of function f.



For how many values of x is f not differentiable over the interval (–4, 4)?

Answers

Answer:

4

Step-by-step explanation:

In the graph of the function, between the interval (-4, 4), there are 4 values of x for which the given function is not differentiable.

What is implicit differentiation?

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,
The function from observation seems to be a discontinuous function,
And the function is not differentiable at x = -1, 0, 1, and 3.
So there are 4 points in the interval (-4, 4) where the function is not differentiable.

Thus, In the graph of the function, between the interval (-4, 4), there are 4 values of x for which the given function is not differentiable.

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I’m stuck but the next drop down is above or below

Answers

Answer:

less; below

Step-by-step explanation:

We can change both fractions to improper fractions first for easier comparison.

-[tex]\frac{7}{5}[/tex] = -

-1[tex]\frac{1}{5}[/tex] = -[tex]\frac{5}{5}[/tex] -

-1[tex]\frac{1}{5}[/tex] = -[tex]\frac{6}{5}[/tex]

As you can see, -[tex]\frac{7}{5}[/tex] has a higher absolute value but both fractions are negative so it has a lesser value than -[tex]\frac{6}{5}[/tex] and thus would also be below -[tex]\frac{6}{5}[/tex].

Use the figure and follow the directions below.

Answers

f is the vertex of 1

Seaver Books, a small book publishing company, wrote off the debt of The Learning Center, and the Academy of Basic Education, both small private schools, after it determined that the schools were facing serious financial difficulty. No notice of the action was sent to the schools; Seaver Books simply stopped sending bills. Nearly a year later, The Learning Center was given a large endowment and a government grant. The resulting publicity brought the school to the attention of Seaver Books, which immediately reinstated the account, and sent a new bill to the school, including interest for the entire time the debt was outstanding. No further action was taken regarding the Academy of Basic Education, which was still operational. Did Seaver Books act ethically in reinstating the debt of one client, and not the other? Explain.

Answers

Answer:

Seaver Books and Ethical Practice

Yes.  Seaver Books acted ethically in reinstating the debt of The Learning Center and not that of the Academy of Basic Education.

Step-by-step explanation:

Writing off a doubtful debt or account is a determination that is done on a case-by-case basis.  When a customer's ability to repay a debt is in doubt, the reasonable act will be to write off the debt from the balance to ensure prudent accounting.  When the customer's ability to settle the debt is reassessed to be favorable, the debt can be reinstated accordingly.  However, it is better to restate the debt after the customer has settled the account and not before.  The good news is that customers are not usually informed that their accounts have been written off as doubtful and need not be informed of the reinstatement.

Rank the following tools for measuring length from those that give the least precise results to the most precise results.

Highway mile marker

A yardstick

A length of a person's foot

A five - foot long branch from a tree​

Answers

Answer:

option 3,4,2,1

Step-by-step explanation:


Highway mile marker

A five - foot long branch from a tree

A length of a person's foot

A yardstick

If a spider can move 1/2 of a mile every hour, then how many hours would it take for a
spider to go 4 miles?

Answers

Answer:

2

Step-by-step explanation:

   1/2x4=2

“How mathematics is involved in Merchandising?”

Answers

Answer:

You have to have the number of items you paid for and know what numbers you're calculated at checkout.

1 2/3 X 2 5/8

Please helo

Answers

Answer:

The answer in whole number form is  4 5/8

Step-by-step explanation:

Jerome wants to rent a car for 8 days, and he's interested in the collision damage waiver but not the loss damage waiver. If the daily rate is $60 and CDW is $66, what is his total rental cost?

A$588

B$480

C$546

D$1008

Answers

Answer:

c?

Step-by-step explanation:

Answer:

C.546

Step-by-step explanation:

60×8=480+ 66=546

What is the sum of three hundredths plus two?

Answers

.3 tenths .03 hundredths...

Add two-2

.03 + 2

2.03

I feel like this isn’t the answer your looking for, perhaps you worded the question wrong?

Answer:

2.03

Step-by-step explanation:

9err9jwihwr9ihwrighiwrrghihsrhrgishfgisif10101

Answers

Answer:

yes

Step-by-step explanation:

...

Paula knows the total cost for 100 students will be $750, and the cost total cost for 150 students is $1050. What is the caterer’s fixed cost and the rate per student served?

Answers

Step-by-step explanation:

the price charged for 100 students reflects the cost per student that applies to the order as a whole.

100 * 6 = $600, so the fixed cost is 750-600 = 150.

...

We can check this by substituting in the other equation.

Does 150*6 + 150 = 1050?

150*6=900

900+150 = 1050.

Yes, it does

...

We can express this relationship by the equation:

y = mx + b

where

y = total cost

m = $6 per student

x = number of students

b = fixed costs = 150

y = 6x + 150

The caterer’s fixed cost and the rate per student served is $6 and $150

How to choose what quantity to multiply the first equation?

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

[tex]a_1x + b_1y = c_1\\a_2x + b_2y = c_2[/tex]

then, if we want to eliminate variable x, then we have to multiply equation 1 with

[tex]-\dfrac{a_2}{a_1}[/tex]

which will make coefficient of x in first equation as

[tex]a_1 \times - \dfrac{a_2}{a_1} = -a_1[/tex]

Then adding both equation will eliminate the variable x.

Given;

Cost of 100 students= $750

Cost of 150 students= %1050

Let the fixed cost of caterer be x

and the cost per student be y

x+100y=750...(1)

x+150y=1050...(2)

solving the above equations;

50y=300

y=6

x=750-600=150

The fixed cost is $150, while the per-student cost is $6.

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Principal=$100, Rate: 5% , Time: 3yrs, INTEREST?

Answers

Answer:

really sorry

Step-by-step explanation:

u

Answer:

Is this a question?

Step-by-step explanation:

If it is, I will answer in the comments if i can

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