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
Morgarella [4.7K]
3 years ago
6

At what values of x does f(x) = x^3 - 2x^2 -4x+1 satisfy the mean value theorwm on [0,1]

Mathematics
1 answer:
denis-greek [22]3 years ago
4 0

Answer:

x=1/3

Step-by-step explanation:

A function f is given as

f(x) = x^3-2x^2-4x+1 in the interval  [0,1]

This function f being an algebraic polynomial is continuous in the interval [0,1] and also f is differntiable in the open interval (0,1)

Hence mean value theorem applies for f in the given interval

f(1) = 1-2-4+1 = -4\\f(0) = 1

The value

\frac{f(1)-f(0)}{1-0} =\frac{-4-1}{1} =-5

Find derivative for f

f'(x) = 3x^2-4x-4

Equate this to -5 to check mean value theorem

3x^2-4x-4=-5\\3x^2-4x+1=0\\\\(x-1)(3x-1) =0\\x= 1/3 : x = 1

We find that 1/3 lies inside the interval (0,1)

You might be interested in
Can someone answer this? 27/12 + 3/? = 21/8 (
allsm [11]
50 becacause there is 27 and you need to add it all together
8 0
3 years ago
Dominic's water jug holds 1.25 quarts. Terrell says he can find the capacity of the jug in fluid ounces by dividing 1.25 by 32.
maks197457 [2]
Yes,because there are 32 fl oz in a quart, so Terrell is correct.
7 0
3 years ago
Read 2 more answers
Find (2)(‐3) pleease
Anna11 [10]

Answer:

-6

Step-by-step explanation:

PLEASE GIVE BRAINLIEST

4 0
2 years ago
Read 2 more answers
Help me my grade depends on this
taurus [48]

Answer:

If it’s asking what it is before the tax, it’s just $25.20.  With the tax, it’s $26.46

Step-by-step explanation:

3 0
1 year ago
Read 2 more answers
Multiply the following: show your SOLUTIONS
abruzzese [7]
The answer for the problems are below in the picture let me know if that makes sense.

5 0
2 years ago
Other questions:
  • If a 4 x 16 rectangle has the same area as a square, what is the length of a side of the square?
    5·2 answers
  • Which is the angle measure represented by 2 rotations counterclockwise?
    15·1 answer
  • In a survey of 500 voters 430 said they would vote the same candidate again. What percent of the voters would vote the same way
    9·2 answers
  • This scatterplot and regression line below show the relationship between the average rent for a 1-bedroom apartment in New York
    13·1 answer
  • Mr. Singleton wants to buy a new television. The regular price is $999. The store is offering a 25% discount and a sales tax of
    14·1 answer
  • Please help me on this will give you brainliest!!
    14·1 answer
  • 2 pounds of grapes cost $8 How do they cost per pound? How many pounds of grapes do you get per dollar?
    6·1 answer
  • Please Help! Need this to pass :/
    11·1 answer
  • Will rounding to the nearest 10 0r 100 give a closer estimate of 748-431?
    10·2 answers
  • Domain and range: identify the domain and range of the function.​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!