Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = f (b) − f (a) b − a . If the Mean Value Theorem cannot be applied, explain why not.

f(x) = x^3 + 2x, [-1,1]

Answers

Answer 1

Answer:

There is a value of [tex]c[/tex] in (-1, 1), [tex]c = 0.577[/tex].

Step-by-step explanation:

Let [tex]f(x) = x^{3}+2\cdot x[/tex] for [tex]x \in[-1,1][/tex], we need to prove that [tex]f(x)[/tex] is continuous and differentiable to apply the Mean Value Theorem. Given that [tex]f(x)[/tex] is a polynomical function, its domain comprises all real numbers and therefore, function is continuous.

If [tex]f(x)[/tex] is differentiable, then [tex]f'(x)[/tex] exists for all value of [tex]x[/tex]. By definition of derivative, we obtain the following expression:

[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} \frac{(x+h)^{3}+2\cdot (x+h)-x^{3}-2\cdot x}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} \frac{x^{3}+3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot x+2\cdot h-x^{3}-2\cdot x}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} \frac{3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot h}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} 3\cdot x^{2}+ \lim_{h \to 0} 3\cdot x \cdot h+ \lim_{h \to 0} h^{2}+ \lim_{h \to 0} 2[/tex]

[tex]f'(x) = 3\cdot x^{2}+2[/tex] (Eq. 2)

The derivative of a cubic function is quadratic function, which is also a polynomic function. Hence, the function is differentiable at the given interval.

According to the Mean Value Theorem, the following relationship is fulfilled:

[tex]f'(c) = \frac{f(1)-f(-1)}{1-(-1)}[/tex] (Eq. 3)

If we know that [tex]f(-1) = -3[/tex], [tex]f(1) = 3[/tex] and [tex]f'(c) = 3\cdot c^{2}+2[/tex], then we expand the definition as follows:

[tex]3\cdot c^{2}+2 = 3[/tex]

[tex]3\cdot c^{2} = 1[/tex]

[tex]c = \sqrt{\frac{1}{3} }[/tex]

[tex]c \approx 0.577[/tex]

There is a value of [tex]c[/tex] in the interval (-1, 1), [tex]c = 0.577[/tex].


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tysm

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Answer: y=15/4x+35/4

Step-by-step explanation:

Given a function described as equation y = 3x + 4, what is y when x is 1,2, and 3

Answers

Answer:

when x=1 y=7, when x=2 y=10, when x=3 y=13

Step-by-step explanation:

HELP ME ASAP

graph f(x)=3x+4 and h(x)=f(x+3)

Answers

sorry if it’s the wrong answer

The standard form for expressing the equation of a straight line is

y = mx + b

Given the functions from the question f(x)  = 3x + 4

If h(x) = f(x+3)

Replace x with x+3 in the function f(x) to have;

h(x) = 3(x+3) + 4

h(x) = 3x + 9 + 4

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What is J/-12 > 9??​

Answers

Answer:

j > - 108

Step-by-step explanation:

Step 1:

j / - 12 > 9          Equation

Step 2:

j > 9 × - 12         Multiply - 12 on both sides

Answer:

j > - 108

Hope This Helps :)

Answer:

j<−108

Step-by-step explanation:

j

−12

>9

Step 1: Simplify both sides of the inequality.

−1

12

j>9

Step 2: Multiply both sides by 12/(-1).

(

12

−1

)*(

−1

12

j)>(

12

−1

)*(9)

j<−108

Answer:

j<−108

solve (x-4)^2=5.
Answers:
A. x=9 and x=1
B. x=5+(square root)4
C. x=-4+(square root)5
D. x=4+(square root)5

Answers

Answer:

don't dout yourself

Step-by-step explanation:

never give up thanks for the free points

What is the value of the function at x=−2?

Answers

Answer:

y = 3

General Formulas and Concepts:

Reading a Cartesian PlaneReading and labeling coordinates

Step-by-step explanation:

The question is asking us what the y-value is when x = -2.

According to the graph, when x = -2, y = 3.

Therefore, y = 3.

If a coconut has tree has 12 coconut on it if 25% of the coconuts fell to the ground how many fell

Answers

Answer:

It would be three coconuts hope this helped

Step-by-step explanation:

Please help.

Solve the System of Equations by Graphing

y=4

3x+4y=4

Answers

Answer:

graph below

Step-by-step explanation:

Graph in image below

giving 30 points &’ brainliest to whoever can help w there two questions!!

Answers

Answer:

binomial and not a polynomial

Find the slope of the line.

Answers

The slope of the line should be -3/2

PLEASE HELP MEEEE!!!!! Marcos had 15 coins in nickels and quarters total amount of those coins is $2.25. How many quarters and dimes he has?

Answers

Answer:

try 15 / 2.25

Step-by-step explanation:

Write an expression to model the following situation: A submarine was 32 m below sea level. It descended 28 more meters.

What is its new position below sea level?

32 + 28


32 – 28

–32 + 28

–32 – 28

Answers

it would be -32-28 please mark brainliest

Suppose 420 randomly selected people are surveyed to determine whether or not they play sports. The sample proportion for successes is determined to be p′=0.393 and the sample proportion for failures is q′=0.607. What is the 95% confidence interval for the proportion of the population who play sports? z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576 Use the table of common z-scores above. Round the final answer to three decimal places.

Answers

Answer:

420 funny number

Step-by-step explanation:

M=3 (-4,-7) PLease include steps!!( I will give brainliest)

Answers

Answer:

65

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Simplify
114
11
1
1112
01
114
0 114
0 11 12

Answers

The answer is A. Im not exactly sure how to get there I just plugged it into my calculator.

In science class, Polly learned that trees help make the oxygen that people breathe. One tree makes about 250 pounds of oxygen each year. Polly wonders how much oxygen the trees on her street make. When she gets home, she counts 32 trees on her street. How many tons of oxygen do they make in a year?

Answers

Answer:

They make 4 approximately tons of oxygen each year.

Step-by-step explanation:

( 250lbs × 32 ) ÷ 2000 = 4t

250 pounds because each tree makes about 250 pounds of oxygen a year.

× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.

÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.

There are a total of 120 bicycles and tricycles in a shop. There are 302 wheels in allmany bicycles and how many tricycles are in the shop?

Answers

Answer: There are  62 tricycles in the shop.

Step-by-step explanation:

Given: Number of wheels in a bicycle = 2

Number of wheels in a tricycle = 3

Let x = Number of bicycles , y = Number of tricycles.

As per given , we have

x+y =120       (i)

2x+3y=302       (ii)

Multiplying 2 on both sides of (i)

2x+2y=240      (iii)

Subtract (iii) from (ii) , we get

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Hence, there are 58 bicycles and 62 tricycles in the shop.

C
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8zft
, how many pieces can Kris cut?

Answers

Answer:

4

Step-by-step explanation:

because 2+2+2+2=8 pretty self explanatory

Answer:

13

Step-by-step explanation:

If the area of the rectangle is(xA^3−4x^2−15x+21) and the width is (x-6), what is the length?

Answers

Answer:

hmm, imma have to do the problem

Step-by-step explanation:

what is 2/3 divdided by 1/6

Answers

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

A line passes through the point (-6,7) and has a slope of -4/3. Write an equation in slope-intercept form for this line.

Answers

Answer:

Step-by-step explanation:

y-7= -4/3 (x+6)

y-7= -4/3x-8

add 7 to both sides

y= -4/3x-1

The equation in slope-intercept form for the given line is 3y = -4x -3

What is Equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that a line passes through the point (-6,7) and has a slope of -4/3.

Standard equation of a line = y = mx + c where m is the slope,

Therefore, putting values of x and y to get the value of c

7 = -6*-4/3 + c

c = 7 - 8

c = -1

Equation = y = -4x/3 -1

Or, 3y = -4x -1

Hence, the equation of a line passing through the point (-6,7) and has a slope of -4/3 is 3y = -4x -1

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Hadley paddled a canoe 2 miles in 1/9 of
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Answers

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Answer:

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Step-by-step explanation:

- They are both 3 dimensional

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Answers

Answer:

Step-by-step explanation:

Given principal p =$3500

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=7000×2.3/100

=16100/100

=161.

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Answers

Answer:

Sasha stopped working at 12:10 PM

Step-by-step Explanation

8:30 + 3 hours and 40 minutes = 12:10 PM

Mark as brainliest if it's right!

Answer:

12:10 p.m

Step-by-step explanation:

3 hours from 8:30 is 11:30 a.m.

Now we add 30 minutes to 11:30 and you get 12:00

Add the remaining 10 minutes and you get 12:10 p.m

I hope this helped, please mark Brainliest, thank you!

about how many 18s are there in 250?a.10 b.12 c.15​

Answers

Answer:

C. 15

Step-by-step explanation:

It's 13.888 about 14, so 15 is the closest answer.

b

Step-by-step explanation:

taking 250÷18=13.88~

Raju bought a book for Rs.35.65. He gave Rs.50 to the shopkeeper. How much money did he get back from the shopkeeper?​

Answers

I Hope this helps u out

Helpppppppp pleaseeeee

Answers

Answer:

108 cm^2

Step-by-step explanation:

A= 1/2 b×h

so

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9a + 8 - 20-3-50
Answer

Answers

Answer:

9a-65

Step-by-step explanation:

simply write 9a+(add the remaining numbers all together)

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