PLEASE HELP
The table above gives selected values for the differentiable function f. in which of the following intervals must there be a number c such that f’(c)=2 PHOTO ATTACHED

PLEASE HELPThe Table Above Gives Selected Values For The Differentiable Function F. In Which Of The Following

Answers

Answer 1

Answer:

C.

Step-by-step explanation:

We need to apply Mean Value theorem here.

We just need to calculate the average rate of change for each interval.

A) x=0 to x=4

We have the points (0,8) and (4,0) are the points that correspond to the endpoints of the given interval.

(8-0)/(0-4)

8/-4

-2

Not this choice

B) x=4 to x=8

We have the points (4,0) and (8,2) are the points that correspond to the endpoints of the given interval.

(2-0)/(8-4)

2/4

1/2

Not this choice

C) x=8 to x=12

We have the points (8,2) and (12,10) are the points that correspond to the endpoints of the given interval.

(10-2)/(12-8)

8/4

2

This one works.

D) x=12 to x=16

We have the points (12,10) and (16,1) are the points that correspond to the endpoints of the given interval.

(1-10)/(16-12)

-9/4

Answer 2

The table is an illustration of mean value theorem

[tex]\mathbf{f'(c) =2}[/tex] on the interval (8,12)

If a function is differentiable, then:

[tex]\mathbf{f'(c) =\frac{f(b) - f(a)}{b - a}}[/tex]

(a) (0,4)

This gives

[tex]\mathbf{f'(c) =\frac{f(4) - f(0)}{4 - 0}}[/tex]

[tex]\mathbf{f'(c) =\frac{f(4) - f(0)}{4}}[/tex]

From the table, we have:

[tex]\mathbf{f'(c) =\frac{0 - 8}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{- 8}{4}}[/tex]

[tex]\mathbf{f'(c) =-2}[/tex]

(b) (4,8)

This gives

[tex]\mathbf{f'(c) =\frac{f(8) - f(4)}{8 - 4}}[/tex]

[tex]\mathbf{f'(c) =\frac{f(8) - f(4)}{4}}[/tex]

From the table, we have:

[tex]\mathbf{f'(c) =\frac{2-0}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{2}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{1}{2}}[/tex]

(c) (8,12)

This gives

[tex]\mathbf{f'(c) =\frac{f(12) - f(8)}{12 - 8}}[/tex]

[tex]\mathbf{f'(c) =\frac{f(12) - f(8)}{4}}[/tex]

From the table, we have:

[tex]\mathbf{f'(c) =\frac{10-2}{4}}[/tex]

[tex]\mathbf{f'(c) =\frac{8}{4}}[/tex]

[tex]\mathbf{f'(c) =2}[/tex]

Hence, [tex]\mathbf{f'(c) =2}[/tex] on the interval (8,12)

Read more about mean value theorems at:

https://brainly.com/question/3957181


Related Questions

I’ll give brainliest and a 100 points

Answers

Answer:

130.5ft²

Step-by-step explanation:

Hello There!

The figure shown is a composite figure ( so we can't find the area of it using one formula )

That being said we want to break the irregular figure into regular figures in which the area can simply be found using a formula

The figure would be broken in to the following shapes

A rectangle with a width of 4 ft and a length of 9 ft

A rectangle with a width of 8 ft and a length of 9 ft

A triangle with a height of 5 ft and a base of 9 ft

Now that we have broken the irregular figure into regular shapes we want to find the area of each individual shape

For the smaller rectangle:

The area of a rectangle can simply be calculated by multiplying the width and length

So A = 9 * 4

9 * 4 = 36

so the area of the smaller rectangle is 36ft²

For the larger rectangle

Once again the area can simply be found by multiplying the width and length

A = 8 * 9

8 * 9 = 72

so the area of the larger rectangle is 72ft²

For the triangle

To find the area of a triangle we want to use this formula

[tex]A = \frac{bh}{2}[/tex]

where b = base and h = height

We have already identified the base and height so all we have to do is plug in the values into the formula

[tex]A=\frac{5*9}{2} \\5*9=45\\\frac{45}{2} =22.5[/tex]

so the area of the triangle is 22.5ft²

Finally we add the areas of each regular figure

22.5 + 72 + 36 = 130.5

so we can conclude that the area of the composite figure is 130.5ft²

Complete the transformations below.
Then enter the final coordinates of the figure.
A(-3,4)
B(1,2)
C(-2,1)
A'' (-6, [?])
B'' ([],[])
C"" ([],[]).
1) Reflect across X - axis
2 <1, -3>
3) Dilate K = 3

Answers

Answer:

B'''(6, -15), C'''(-3, -12)

Step-by-step explanation:

For point B,

[tex]B(1,\,2) \to B'(1,\,-2) \to B''(2,\,-5) \to B'''(6,\,-15)[/tex]

For point C,

[tex]C(-2,\,1) \to C'(-2,\,-1) \to C''(-1,\,-4) \to C'''(-3,\,-12)[/tex]

Reflecting a point across the x-axis:  leave the x-coordinate the same; replace the y-coordinate with its opposite.

<1, -3>  These are translations: add 1 to x, subtract 3 from y.

Dilate k=3:  multiply both x and y by 3.

PLEASE HELP THIS IS DUE I HAVE BEEN TRYING AND DONT UNDERSTAND IT!!!!

Answers

Answer:

Step-by-step explanation:

Moving a coordinate left will subtract from the x coordinate (left 3 means subtract 3 from x coordinate)

Moving a coordinate right will add to the x coordinate (right 3 means add 3 to x coordinate)

Moving a coordinate down will subtract from the y coordinate (down 3 means subtract 3 from y coordinate)

Moving a coordinate up will add to the y coordinate (up 3 means add 3 to y coordinate)

Reflect means flip the sign of the corresponding coordinate

reflect over x axis flip the sign of x coordinate

reflect over y axis flip the sign of y coordinate

g(x)=2x-x when x=-5
What is the answer to this please solve

Answers

9514 1404 393

Answer:

  -5

Step-by-step explanation:

The given linear equation simplifies to ...

  g(x) = 2x -x

  g(x) = x

For x = -5, this is ...

  g(-5) = -5

A shop is selling notebooks for £1.50 each. They have a buy one get one free offer on. How many notebooks can be brought for £22?

Answers

Answer:

28

Step-by-step explanation:

22÷1.50=14.6

=14

14×2=28

Please help giviing brainliest!!!

Answers

Answer:

2 1/2 x 3 1/2 x 7 =  61 1/4

A= 61 1/4

Hope I helped a bit

the more you take the more you leve behind​

Answers

Answer:

Footsteps is the answer.

Hope it helps!!!

Value of X. Please give step by step so I understand

Answers

Answer:

The value of x is 15.

Step-by-step explanation:

Since the base is 40 inches long, and the two triangles are congruent - both are right triangles and have sides x and their bases equal - you know that each base of a triangle is 20 inches long. Using the Pythagorean Theorem, you can get that [tex]x^2+20^2=25^2[/tex]. Solve for x by isolating the variable on one side: [tex]x^{2} =25^{2} - 20^{2}[/tex] ⇒ [tex]x^{2} = 625 - 400[/tex] ⇒ [tex]x^{2} = 225[/tex] ⇒ [tex]x^{2} =225[/tex] ⇒ [tex]x=\sqrt{225}[/tex] ⇒ [tex]x=15[/tex] inches.

Help me out here.........

Answers

Answer:

G. 10.5 pounds

Step-by-step explanation:

96 oz + 72 oz = 168 oz

There are 16 oz in one pound

168 oz / 16 oz = 10.5 pounds.

Please be sure to mark this as brainliest if it helpd you!

Answer:

Step-by-step explanation:

Total ounces = 96 + 72 = 168 ounces

1 ounce =

0.0625 pound

168 ounces = 10.5 pound

Option G is the correct answer

A man bought 5 laptops and a desktop for taka 229600. If a laptop costs taka 32750 find the cost of the desktop

Answers

Answer:

65850

Step-by-step explanation:

Answer:

65,850

Step-by-step explanation:

5 laptops costs 163,750(5x32750). Total costs of 229,600-laptops 163,750=costs of desktop 65850.

Does the mapping diagram represent a function? Why or why not?

Answers

Answer:

If I was you I can go

for A because the function name is one to many

how would you know if a polynomial is prime?

Answers

Prime polynomial cannot be factorized into the product of two polynomials of lesser degree. Example: x2+x+1. Good luck.

Whats 9x6 pls helpppppllll








Answers

if you do your multiplication it is 54

Answer:

54

Step-by-step explanation:

simplify 4 1/4 hours:45 minutes​

Answers

Answer:

[tex]4\frac{1}{4}[/tex] hours : 45 minutes

[tex]4\frac{1}{4}[/tex] hours : [tex]\frac{3}{4}[/tex] hours

255 minutes : 45 minutes

Answer:

49 1/4

Step-by-step explanation:

4 1

4

+ 45

=  (4 + 45) + (  

1

4

+ 0 )

=  49 +  

1

4

+ 0 × 4

=  49 +  

1

4

+  

0

4

=  49 +  

1 + 0

4

=  49 +  

1

4

=  

49 1

4

Which of the following angle pairs
are
NOT congruent?

Answers

Answer:

<2 and <8

Step-by-step explanation:

the number of bacteria present in a culture after t minutes is given as b=10e

Answers

Answer:

Step-by-step explanation:

I have no clue I just need 5 pionts

Help me & like actually answer instead of putting the link thing cause I don’t know how to do that lol please & thank you :)

Answers

Answer:

f(x) = 120+15x

Step-by-step explanation:

the constant is 120 because that is the money that he already has and is an unchanged quantity. for every week he gains $15. that means that he gains 15x after x weeks.

Help me plz it’s important

Answers

Is it Im1,im2, 1m3??

A laundry basket contains 9 socks, of which 3 are blue.

What is the probability that a randomly selected sock will be blue?

Write your answer as a fraction or whole number.
P(Blue) = ?

Answers

Answer:

3

Step-by-step explanation:

Which equation has a slope of –2 and passes through the point (5, 0)?
A. y = 2x + 5
B. y = 2x + 10
C. y = –2x + 5
D. y = –2x + 10

Answers

Answer:

D. y = –2x + 10  

Step-by-step explanation:

1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].  

Since [tex]m[/tex] represents the slope, substitute -2 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (5,0) into the formula as well. This gives the following equation:

[tex]y - 0 = -2(x-5)\\y = -2(x-5)[/tex]

2) Expand the right side of the equation to find the answer:

[tex]y = -2(x-5)\\y = -2x+10[/tex]

So, option D is correct.

17. Which economic instability becomes a problem during a recession?
A. Producer Price Index
B. Inflation
C. Unemployment

Answers

Please report this link please

Find sin 0
16
20
A.
В.
C.
D.
13

Answers

Answer:

dont know im sorry

Step-by-step explanation:

i believe the answer is b. good luck.

select all expression that are equivalent to 64 2/3.

Answers

Answer:

Option B and D

Step-by-step explanation:

As,

[tex] {64}^{ \frac{2}{3} } = {(\sqrt[3]{64})}^{2} = \sqrt[3]{ {64}^{2} } [/tex]

Find a polynomial that has the given degree and zeros.

Degree 3 with -1, 3, and -5 as zeros

[tex]x^{3} + {?}x^{2} + {?}x + {?}[/tex]

Answers

You can write such a cubic polynomial in terms of its roots using the factor theorem:

(x - (-1)) (x - 3) (x - (-5)) = (x + 1) (x - 3) (x + 5)

Now just expand this:

(x + 1) (x - 3) (x + 5) = x ³ + (1 - 3 + 5) x ² + (-3 + 5 - 15) x - 15

… = x ³ + 3x ² - 13x - 15

un campo de fútbol mide de largo 105m y de ancho 65m¿cuál es el área total del campo de fútbol?​

Answers

Answer:

6825

Step-by-step explanation:

area=largo X ancho

area= 105 x  65=  6825

Help plss
2. This is Josh’s solution for the equation :

Is Josh’s solution correct? Explain.

Answers

Answer:

x = 7

Step-by-step explanation:

in Josh solution, the steps are correct till

(x-3)² = 16. After this

√(x-3)² = √16

x-3 = 4

x = 4+3 = 7

No, Josh is incorrect the roots of the quadratic equation are 19 & -13.

What is a quadratic equation ?

An equation is quadratic in form if it can be written in the form of ax + bx + c = 0, where a, b, and c are constants and x is the variable.

Given that,

The quadratic equation,

x²  - 6x - 7  = 0

we can calculate the roots of the equation by using the formula:

x   = -b + √(b² - 4ac) / 2a

In the given equation,

a = 1

b = -6

c = -7

x  = -(-6)  + √((-6)² - 4x1x(-7)) / 2

  =    (6 + 8)/ 2

x =   7,  -1

Hence, Josh's solution is not correct.

To know more about quadratic equation check:

https://brainly.com/question/30098550

#SPJ3

Circles Test

Find the circumference of each circle. Round your answer to the nearest whole

Answers

Ejrkgodwvekgpfiahwltofieuw 28348381

CAN SOMEONE PLEASE HELP ME

Answers

Answer:

[tex]12.3[/tex]

Step-by-step explanation:

[tex]\bar{x}=\frac{6+17+15+11+10+9+18}{7}=12.3[/tex]

MAJOR HELP PLSSS!!!!!
Young company expects to double their profits every year for the next 10 years. If their profits were $5000 this year, which expression represents the profits after 10 years

A.5,000x2x10

B.5,000x2^10

C.5,000^2x10

D.5,000^10

Answers

Answer:

Suppose profits were $1

At 1 yr profit = 2    (2)^1

    2 yr         = 4     (2)^2

    3 yr         = 8      (2)^3

    10 yr        = 1024    (2)^10

So the correct answer should be  5000 * (2)^10

HELP ME PLS!!!

I need help :(

Answers

Answer:

Step-by-step explanation:

Remark

I nearly found the length of a chord PQ. Be careful you don't make the same mistake. It is an arc which is part of the circumference.

Equation

Length of arc PQ = angle/360  * 2* pi * r

Givens

Angle = 110

r = 4 in

Solution

Length of arc PQ = 110/360  * 2 * 3.14 * 4

Length of arc PQ = 0.305555 * 6.28 * 4

Length of arc PQ = 7.67555

Length of arc PQ = 7.68

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