How do I Determine whether Rollie's theorem can be applied to F on the closed interval (AB) F of X = -x squared

Answers

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Your question is incomplete. I will take the complete question as:

[tex]f(x) = -x^2[/tex]

[tex]Interval: [-1,1][/tex]

Required

Determine whether Rollie's theorem can be applied or not

First, find the coordinates of the endpoints on the closed interval [-1, 1]

[tex]f(x) = -x^2[/tex]

[tex]f(-1) = -(-1)^2 = -1[/tex] ------ [tex](-1,-1)[/tex]

[tex]f(1) = -(1)^2 =-1[/tex] ---- [tex](1,-1)[/tex]

Find the derivative of f(x)

[tex]f(x) = -x^2[/tex]

[tex]f'(x) = -2x[/tex]

Calculate the slope (m) of the secant line i.e. [tex](-1,-1)[/tex] and [tex](1,-1)[/tex]

[tex]m = \frac{-1 - (-1)}{1 - (-1)}[/tex]

[tex]m = \frac{-1 +1}{1 +1}[/tex]

[tex]m = \frac{0}{2}[/tex]

[tex]m=0[/tex]

Set the derivative to the calculated slope:

[tex]f'(x) = m[/tex]

[tex]-2x = 0[/tex]

[tex]x=0[/tex]

Plug in 0 for x in f'(0)

[tex]f'(x) = -2x[/tex]

[tex]f'(0) = -2 * 0[/tex]

[tex]f'(0) = 0[/tex]

Since f'(0) is differentiable at x = 0. We can conclude that Rollie's theorem can be applied


Related Questions

Latrell wants to fill his water bottle between classes, but the water fountain next to his classroom is frustratingly slow. It takes Latrell 5 seconds to get each ounce of water in his bottle. There is a proportional relationship between the amount of water (in ounces) Latrell puts in his water bottle, x, and how long in seconds) it takes to get that amount, y. Graph this relationship. Select two points to draw a line.

what is the slope of the line? _____​

Answers

Answer:

Step-by-step explanation:

Slope = rise/ run, or y∨2 - y∨1/ x∨2 - x∨1

5-10/ 1-2 =

-5/-1 = 5

The slope of the line drawn from the given data is 5.

What is the slope?

A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Given this, Latrell fills his bottle with one ounce of water in five seconds. The amount of water Latrell puts in his water bottle (in ounces), x, and the time (in seconds) it takes to get that amount, y, are proportionate. This connection can be graphed. Since, the line will pass from the origin(0, 0).

Since given y is the directly proportional equation of the line will be;

y = mx

where m is the slope of the line

Also given, filling the bottle at every ounce requires 5 seconds of time. hence, the line will go from (1, 5)

Thus, the value of the m will be;

5 = m *1

m =5

Therefore, the slope of the line is 5.

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Find the measure of the indicated angle

Answers

Answer:

x = 7

angle (7x + 8) = 57 degrees

Step-by-step explanation:

all triangles interior angles add up to 180 degrees.

(7x+8) + 90 + 33 = 180

7x+8 = 57

7x = 49

x = 7

(7x + 8) = 57

Answer:

57 degrees

Step-by-step explanation:

7x+8+33=90

7x=90-8-33

=90-41

7x=49

x=7

3.(x + 2) + (2x + 3) = 23

Answers

Answer:

x = 6

Step-by-step explanation:

(x + 2) + (2x + 3) = 23

Combine like terms

3x +5 = 23

Subtract 5 from each side

3x+5-5 = 23-5

3x = 18

Divide each side by 3

3x/3 = 18/3

x = 6

Answer:

x = 6

Step-by-step explanation:

1. Remove parentheses where unneeded. x + 2 + 2x + 3 = 23

2. Add constants. x + 5 + 2x = 23

3. Combine like terms. 3x + 5 = 23

4. Subtract "5" from the constants on both sides of the equation. 3x = 18

5. Divide both sides by 3. 3x/3 = 18/3

6. Simplify. x = 6

Help please! I really need it! please dont guess if you dont know, dont answer.....( this is basic geometry im just dum'b)

Answers

Answer:

D

Step-by-step explanation:

angles 2 and 6 are corresponding angles and are congruent if the transversal crosses through two parallel lines

Does anyone know how to solve this

Answers

Hey I think the answer is letter b if not
I am sorry

[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Answer:\:\:\:\:\:\:\:\:\:}}}}[/tex]

B. 100°

[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:ChaEunWoo2009\:\:\:\:\:\:\:\:}}}}[/tex]

#CarryOnLearning

plz help math question

Answers

Answer:

y = -2x +20

6x - 5y = 12

Put the value of y in 2nd equation

6x - 5( -2x +20 ) = 12

6x +10x -40 = 12

16x = 12 +40

16x = 52

x = 13/4

Putting the value of x in equation 1

y = -2x +20

y = -2(13/4 ) +20

y = 27/2

Do mark me as brainly. THANKS

A baseball pitcher won 65% of the games he pitched in his career If he pitched 120 games, how many games did he win?​

Answers

Answer:

just do 120 x 0.65

ANSWER: 78

Answer:

78

Step-by-step explanation:

120*0.65=78

Catherine is adding fractions for her homework. Here is some of the work that Catherine has done. 2/3 + 3/5 = 5/8. In the space below, explain the error that Catherine made when adding.

Answers

Step-by-step explanation:

2/3+3/5

=10+9/15

=19/15

The mistake she made was that she didn't took right LCM.

The value of the fraction 2/3 + 3/5 is 19/15.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

2/3 + 3/5

= (10 + 9)/15

= 19/15

Thus,

The value is 19/15.

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uhh solve the question? i hope i find some haikyuu stans out there✌️

Answers

Answer and Step-by-step explanation:

[tex](\frac{1.25 - x}{1.25x} ) * 100\\\\\\(\frac{1.25}{1.25x} - \frac{x}{1.25x} ) * 100\\\\(\frac{1}{x} - \frac{1}{1.25} ) * 100\\\\\frac{100}{x} - 80\\\\\\[/tex]

Decreased by 20%

Answer:

YESSSSSS I LOVE HAIKYUU (my favorite ppl in haikyuu are iwaizumi, akaashi, kuroo, oikawa, and kenma- also suna)

Step-by-step explanation:

also 20% is ur answer

what two numbers multiply to 24 and add 14

Answers

Answer:

its 2 and 12

just basic math lol

Answer:

2 and 12

Step-by-step explanation:

2x12=24

2+12=14

Suppose that a piano costs $5,000 and loses 20% of its value each year. What will be the value of the piano after 16 years? A. $219.90 B. $274.88 C. $140.74 D. $175.92

Answers

The answer is c 140.74 bucks or pound

Based on the information given will be the value of the piano after 16 years is : C. $140.74.

Using this formula

Time=Principal(1-rate)^n

Where:

Principal=$5,000

Rate=20%

Number of year=16 years

Let plug in the formula

Time=5,000(1-0.20)^16

Time=5,000(.80)^16

Time=$140.737

Time= $140.74 (Approximately)

Inconclusion  the value of the piano after 16 years is : C. $140.74.

Learn more here: https://brainly.com/question/23565

After Stan makes a 15% down payment on a $7,000
motorcycle, how much will he still owe?

Answers

1,500 I thinkkkkkkkkk

A phone company charges $67 for monthly access and $14 for each gigabyte of data used. If you sign a two-year contract and use 147.5 gigabytes of data, what is the total amount you will pay for phone service?

Answers

Answer:

the answer is below :)

Step-by-step explanation:

BigBytes will be 100 +10x = y ($100 flat fee plus 10 times the number of gigabytes equals total cost).

GoGig will be 120 + 5x = y.  ($120 flat fee plus 5 times the number of gigabytes equals total cost).

Now set them equal to each other and solve for x to find where the gigabytes are the same.

100 + 10x = 120 + 5x

Subtract 100 from both sides:  10x = 20 + 5x

Subtract 5x from both sides:  5x = 20.

Divide both sides by 5:  x = 4.  4 gigabytes is the answer.

a brainliest would be appreciated :)

The total amount you will pay for phone service is 4 gigabytes.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

BigBytes will be 100 +10x = y

Therefore , We have $100 flat fee plus 10 times the number of gigabytes equals total cost).

GoGig will be 120 + 5x = y.  

We have $120 flat fee plus 5 times the number of gigabytes equals total cost).

Now set them equal to each other and solve for x;

100 + 10x = 120 + 5x

Now Subtract 100 from both sides:  

10x = 20 + 5x

Then Subtract 5x from both sides:

5x = 20.

Now Divide both sides by 5:  

x = 4.  

Hence, the total amount you will pay for phone service is 4 gigabytes.

Learn more about equations here;

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Which of the following shapes is a convex polygon?
OA)
OB)
OC)
OD)

Answers

Answer:

B is a convex polygon cause it points out

pls help
will mark brainliest to who answers first

Answers

Answer:

y=10

x=10

Step-by-step explanation:

THis is isosceles triangle

180-90-45=45

used pyagorous therum thingy

10over2= square root of 200

so c2=asquare X b squared in this case x=y

so 200/2 = 100

x=100square

y=100 square

simplify = 10

Given two angle measures and the length of the included​ side, does this side length affect the number of triangles that can be​ drawn? Explain. ▼ since two angle measures and the length of the included side are​ given, there is ▼ only one more than one way to draw the triangle. The number of triangles that can be drawn is ▼ not affected affected by the length of the given side

Answers

Answer:

Step-by-step explanation:

Since two angles and the length included side is given, we can make only one triangle with this measures. The number of triangles that can be drawn is affected by the length of the given side.

HELLLLLLLLLLLLOOOOOOOO HELPPPPPPP

Answers

Answer:

MARK ME AS BRILLANT ^_^ ~_~

Step-by-step explanation:

how many inches are in a feet

Answers

Answer:

1 foot = 12 inches

Step-by-step explanation:

16d + 20c + 5d -7 - 8c - 7d + 3 Simplify the expression above:

Answers

Answer:

14d + 12c -4

Step-by-step explanation:

John receives $9,500 per month after tax. If his annual gross salary is $120,000, How much does he pay in tax per year?

Answers

John pays $6000 a year in taxes

Hope this helpfully......

but if it's not,im so sorry

A P E X

If each of the numbers in the following data set were multiplied by 18, what would be the new median of the data set? 14, 20, 18, 58, 71, 36

A. 504
B. 360
C. 324
D. 648​

Answers

Answer:

504

step by step : 14x18=252. 20x18=360. 18x18=324. 58x18=1044. 71x18= 1278. 36x18=648. 28x18=504.

Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

504

this killing me pls help ‍♀️

Answers

Answer:

p=-2

Step-by-step explanation:

Start off by adding 3 to both sides:

-6p-3=9

    +3 +3

Now you have this:

-6p=12

Now divide both sides by -6

-6p/-6=12/-6

p=-2

I hope this helps, and have a great day! <3 :)

Answer

-6p - 3 = 9

     + 3 + 3

-6p = 12

 6      6

p = -2

The graph of f(x) = x2 − 3x − 28 is shown. Which of the following describes all solutions for f(x)?

a parabola passing through negative 4 comma zero, zero comma negative 28, and 7 comma zero

(−4, 0), (0, −28), (7, 0)
(−4, 0), (−1, −24), (0, −28), (3, −28), (7, 0)
(x, x2 − 3x − 28) for all real numbers
(x, y) for all real numbers

Answers

Answer:

C. (x, x2 − 3x − 28) for all real numbers

Function graphs are graphs of solution equations for y! In this instance, f(x) = x² -3x -28 is the graph.

Constructing a Function Graph:

⇒f(x) = x² − 3x − 28

A group of all points in the plane of the form (x, f(x)) constitutes the diagram of a function f. The graph of f can also be defined as the graph of an equation y = f(x). As a corollary, a function's graph is a subset of an equation's graph.

Solving equation:

⇒f(x) = x² − 3x − 28

⇒f(x) = x² − (7−4)x − 28

⇒f(x) = x² − 7x+4x − 28

⇒f(x) = x(x −7) +4(x −7)

⇒f(x) = (x −7) (x+4)

Please find the attached file.

Find out more about the graph function here:

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Mel is taking her holidays. She receives $2937.50. This includes her normal pay
and 17.5% leave loading. How much is the leave loading?

Answers

17.5% leaving load
You do 0.0175 divided by the money
$2937.50
———-
0.0175

THIS IS ALSO URGENT- I NEED AN ANSWER ASAP PLS!

Answers

Answer:

c

Step-by-step explanation:

I had to multiply 4 and 3 to get the answer

I am having troubles, would love the help

Answers

Answer:

AC= 12.6

Step-by-step explanation:

The length of AX is half the length of AC. 6.3x2= 12x6

Lee is forming kickball teams that include all of the students who signed up from two schools. Each team must have the same number of players and be from the same school. What is the greatest number of players Lee can put on each team?

Answers

Answer:

The answer is (12 players)

Step-by-step explanation:

2 x 2 x 3 = 12      

36 - 12 = 24

I NEED SERIOUS HELP I AM HAVING MATH EXAM SOON
PLEASEEEEEEEEEE HELP ME IM PREPARING WITH THE PPTS MY TEACHERS HAVE GAVE ME BUT THEY GAVE NO ANSWER AND IM NOT ABLE TO SOLVE THIS(I asked this before itself but never got an answer so with extra details I'm hoping I will get some answers)

Answers

Answer:

Step-by-step explanation:

I need ppl to talk to

Who ever does this for me will get brainly

Answers

Answer:

sorry no can do

Step-by-step explanation:

hehhehehehehehhehe

Some one help please

Answers

6.5. 10 ............
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