1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
NARA [144]
3 years ago
11

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-

separated list. If an answer does not exist, enter DNE.) f(x) = x , [0, 9]
Mathematics
1 answer:
ivanzaharov [21]3 years ago
7 0

Answer:

c = \displaystyle\frac{9}{4}

Step-by-step explanation:

The following information is missing in the given question:

f(x) = \sqrt{x}

Using this we may solve the question as:

We are given the following in the question:

f(x) = \sqrt{x}, x \in [0,9]

We have to find the number c such that f(x) satisfies the Mean value theorem.

Mean Value theorem:

It states that if the function is differentiable in the closed interval [a,b], differentiable in the interval (a,b), then there exist c in (a,b) such that:

f'(c) = \displaystyle\frac{f(b)-f(a)}{b-a}

Now,

f(x) = \sqrt{x}\\f'(x) = \frac{1}{2\sqrt{x}}

Continuity in [0,9]

Since a polynomial function is continuous everywhere, f(x) is continuous in [0,9]

Differentiability in (0,9)

Since a polynomial function is differentiable everywhere the given function is differentiable in interval (0,9)

Then, by mean value theorem:

f'(c) = \displaystyle\frac{f(b)-f(a)}{b-a}\\\\\frac{1}{2\sqrt{c}} = \frac{f(9) - f(0)}{9-0} = \frac{3}{9}\\\\\frac{1}{2\sqrt{c}} = \frac{1}{3}\\\\c= \frac{9}{4}

You might be interested in
If you do these ill give brainliest!! someone smart please help. im struggling
IRISSAK [1]
ANSWER:
15
32
31
10
23
6.5
35
4.8
63
66
200
72
Solution:
Say you have a triangle that is 2.5 by 1
The Number that comes first is the base and there’s only one bass and there’s two sides in those size are 1 so 1×2 is 2+2.5=4.5 so all you’re doing is adding up all the sides together on any shape
4 0
3 years ago
I need help !!! I don’t understand the problem
Pepsi [2]

Answer:

It would be -81²x+81x-18= -9x+6

Step-by-step explanation:

When you work equation one you get 18. Then when you work equation two, you get -2/3=-0.666666667

7 0
4 years ago
If the hypotenuse of a right triangle is 11 and one leg is 2, what is the length of the other leg?
Lelu [443]

Answer:

Step-by-step explanation:

So 11 times 2=22 so you times 11 times 2 on all sides so the answers is 22

5 0
3 years ago
Read 2 more answers
Subtract -7x + 6 from -2x^2 + 9x - 2
JulsSmile [24]

Answer:

( - 2 {x}^{2}  + 9x - 2) - ( - 7x + 6) \\   = - 2 {x}^{2}  + (9 + 7)x + ( - 2 - 6) \\  =  - 2 {x}^{2}  + 16x - 8

4 0
3 years ago
If Z is the centroid of ∆LMN,WZ=4,ZN=14, and ZY = 10, find each missing measure
jeyben [28]

Answer:

ZM = 8

WM = 12

XZ = 7

XN = 21

LZ = 20

Step-by-step explanation:

The centroid of a triangle is the point of intersection of the midpoint of the each of the three sides of a triangle. The centroid of a triangle is located inside the triangle and it is known as the center of gravity.

The centroid theorem for a triangle states that the centroid of a triangle is located at 2/3 of the distance from the vertex of the triangle of the middle of the opposite side.

ZM = (2/3)WM (centroid theorem)

Therefore: WZ = (1/3)WM

WM = 3WZ = 3 * 4 = 12

ZM = (2/3) * WM = 2/3 * 12 = 8

ZN = (2/3)XN (centroid theorem)

XN = (3/2)ZN = 3/2 * 14 = 21

XN = 21

XZ + ZN = XN

XZ + 14 = 21

XZ = 7

LZ = (2/3)LY (centroid theorem)

Therefore: ZY = (1/3)LY

LY = 3ZY = 3 * 10 = 30

LZ = (2/3) * LY = 2/3 * 30 = 20

7 0
2 years ago
Other questions:
  • Arrange these lunch buyers from greatest to least assuming they buy lunch 5 days per week: Alice spends $3 per day, Betty spends
    11·1 answer
  • Yesterday the number of cars sold was 6. the average number of cars sold is typically 10 per day with a standard deviation of 3
    5·1 answer
  • In a recent u.s.census, the population of Illinois was 12,419,293. What is this population after
    12·1 answer
  • Is there an association? Thank you!!
    14·1 answer
  • PLZZZZZZZZZZZZZZZZ HELP ME i begging YOUUUUU !!!!!!!!!!!!!!!!!!!!!!!!!!!
    15·2 answers
  • Write the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.
    9·2 answers
  • Please help with questions.
    15·1 answer
  • Solve the equation by using the quadratic formula.<br> 8x2 – 2x - 15 =0
    9·1 answer
  • What transformation of the parent function f(x) is made to get 4f(x+2)
    8·1 answer
  • Write an algebraic expression that represent the sum of 8 and two-third of x?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!