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
agasfer [191]
3 years ago
15

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e−4x, [0, 2] Yes, it does not m

atter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. No, f is not continuous on [0, 2]. There is not enough information to verify if this function satisfies the Mean Value Theorem. No, f is continuous on [0, 2] but not differentiable on (0, 2). Yes, f is continuous and differentiable on , so it is continuous on [0, 2] and differentiable on (0, 2) . If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0

Answer:

(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

(b) c =0.51995

Step-by-step explanation:

Given

f(x) = e^{-4x};\ [0,2]

Solving (a); Does the function satisfy M.V.T on the given interval

We have:

f(x) = e^{-4x};\ [0,2]

The above function is an exponential function, and it is differentiable and continuous everywhere

Solving (b): The value of c

To do this, we use:

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

In this case:

[a,b] = [0,2]

So, we have:

f'(c) = \frac{f(2) - f(0)}{2 - 0}

f'(c) = \frac{f(2) - f(0)}{2}

Calculate f(2) and f(0)

f(x) = e^{-4x}

So:

f(2) = e^{-4*2} = e^{-8} = 0.00033546262

f(0) = e^{-4*0} = e^{0} = 1

This gives:

f'(c) = \frac{0.00033546262 - 1}{2}

f'(c) = \frac{-0.99966453738}{2}

f'(c) = -0.4998

Note that:

f'(x) = (e^{-4x})'

f'(x) = -4e^{-4x}

This implies that:

f'(c) = -4e^{-4c}

So, we have:

f'(c) = -0.4998

-4e^{-4c} =-0.4998

Divide both sides by -4

e^{-4c} =\frac{-0.4998}{-4}

e^{-4c} =0.12495

Take natural logarithm of both sides

\ln(e^{-4c}) =\ln(0.12495)

\ln(e^{-4c}) =-2.0798

Apply law of natural logarithm

\ln(e^{ax}) =ax

So:

-4c =-2.0798

Solve for c

c =\frac{-2.0798}{-4}

c =0.51995

You might be interested in
A counting number is a multiple of 13 and is also divisible by 4 and 6. What is the smallest number that satisfies these conditi
ASHA 777 [7]

Answer:

39

Step-by-step explanation:

39 is a multiple of 13. 13,26,39.

3+9= 12 which is an even which works both for 6 and 4. 4,8,12. 6,12

8 0
3 years ago
9x - 4y? +72x–24y— 36–0
earnstyle [38]
Not is posible because no exist a igualty
3 0
3 years ago
I do not understand this may I get help?​
ValentinkaMS [17]

Answer:

b

Step-by-step explanation:

the y axis is the axis going up and down, so the reflection would be on the other side of the axis.

5 0
3 years ago
GET 20 PTS AND BE NAMED BRAINLIEST AND GET A THANK U AND A FOLLOW
insens350 [35]
<h3>Therefore 24 students take a car to school. </h3>

Step-by-step explanation:

Given, Total number of students is 80.

and 30% of the total students take a car to school

30% of 80

=\frac{30}{100}\times 80

=24

Therefore 24 students take a car to school.

3 0
3 years ago
What is the common difference for this arithmetic sequence? 45,39,33,27,21,...
Studentka2010 [4]

Answer:

I expect the correct answer

_6

.

6 0
2 years ago
Read 2 more answers
Other questions:
  • Marco wants to set up 12 small turbines with 3 blades each.If 4 wind turbines blades cost $79.64,how much will all the blade cos
    11·2 answers
  • Major arc JL measures 300°. Which describes triangle JLM?
    5·1 answer
  • Camren has a clear container in the shape of a cube. Each edge is 9 centimeters long he found the volume of the container in cub
    10·1 answer
  • The owner of a computer repair shop has determined that their daily revenue has mean​ $7200 and standard deviation​ $1200. The d
    10·1 answer
  • 2x + 5 = 3x + 7<br><br> please help
    6·2 answers
  • A bicyclist rides the same number of miles every minute. The ratio table below shows the number of miles she rides during certai
    5·2 answers
  • Find three ratios that are equivalent to 2 4. A. 8 16 B. 10 24 C. 4 8 D. 3 5 E. 6 12 F. 12 6
    6·1 answer
  • PLEASE ANSWER QUICK!! what’s the correct answer?
    14·1 answer
  • Find the area of the parallelogram.
    9·1 answer
  • Can you please help me translate the argument into symbolic form?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!