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
Alona [7]
2 years ago
14

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 3x2 − 2x + 1, [0, 2] Yes, it do

es not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on . No, f is not continuous on [0, 2]. No, f is continuous on [0, 2] but not differentiab
Mathematics
1 answer:
expeople1 [14]2 years ago
4 0

Answer:

Yes , function is continuous in [0,2] and is differentiable (0,2) since polynomial function are continuous and differentiable

Step-by-step explanation:

We are given the Function

f(x) =3x^2 -2x +1

The two basic hypothesis of the mean valued theorem are

  • The function should be continuous in [0,2]
  • The function should be differentiable in (1,2)

upon checking the condition stated above on the given function

f(x) is continuous in the interval [0,2] as the functions is quadratic and we  can conclude that from its graph

also the f(x) is differentiable in (0,2)

f'(x) = 6x - 2

Now the function satisfies both the conditions

so applying MVT

6x-2 = f(2) - f(0) / 2-0

6x-2 = 9 - 1 /2

6x-2 = 4

6x=6

x=1

so this is the tangent line for this given function.

   

You might be interested in
In Lucille’s class, 35% of the students have blond hair. There are 20 students in the class. How many students have blond hair.
MrRissso [65]

Answer:

7 the answer is 7

Step-by-step explanation:

1. We assume, that the number 20 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 20 is 100%, so we can write it down as 20=100%.

4. We know, that x is 35% of the output value, so we can write it down as x=35%.

5. Now we have two simple equations:

1) 20=100%

2) x=35%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

20/x=100%/35%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 35% of 20

20/x=100/35

(20/x)*x=(100/35)*x       -

20=2.85714285714*x       -

20/2.85714285714=x

7=x

x=7

now we have:

35% of 20=7

we multiply both sides by x

then we divide both sides by 2.85714285714 to get x

3 0
3 years ago
Read 2 more answers
Find the sum of the measure of the interior angles of the polygon below.
lana [24]

Answer:

900

Step-by-step explanation:

(n – 2)180  where n is the number of sides

since this is a 7 sided polygon

(7-2) * 180

5 * 180

900

4 0
3 years ago
José put $1,500 into a savings account. He earns 3% interest every year. How much simple interest will he earn at the end of 3 y
stiv31 [10]

He would have a total of: $1639.09

In intrest alone he would've made 1639.09

Step-by-step explanation:

3%= 0.03

  • The first thing you do is multiply $1,500 by the %3 (0.03).

  • When your done multiplying, you should get 45.

  • Add 45 to 1500

  • Now you have 1545

  • Then you repeat the process over, two more times. However the numbers will change.

7 0
2 years ago
Simplify the following expression 5^2-4/5+2
Sever21 [200]
26 1/5 is the answer i got
8 0
3 years ago
Read 2 more answers
Evaluate the triple integral_E x^6e^y dV where E is bounded by the parabolic cylinder z = 25 - y^2 and the planes z = 0, x = 5,
Nimfa-mama [501]

Nothing crazy here, just a matter of figuring out the limits of integration.

\displaystyle\iiint_Ex^6e^y\,\mathrm dV=\int_{-5}^5\int_{-5}^5\int_0^{25-y^2}x^6e^y\,\mathrm dz\,\mathrm dy\,\mathrm dx

=\displaystyle\int_{-5}^{-5}\int_{-5}^5x^6e^y(25-y^2)\,\mathrm dy\,\mathrm dx

=\displaystyle\left(\int_{-5}^5x^6\,\mathrm dx\right)\left(\int_{-5}^5e^y(25-y^2)\,\mathrm dy\right)=\boxed{\frac{625,000(3+2e^{10})}{7e^5}}

4 0
3 years ago
Other questions:
  • The line y=-1/3x+4 passes through which of the following points
    9·2 answers
  • Write in word form 337,173
    12·2 answers
  • Latoya made $306 for 17 hours of work.
    11·2 answers
  • If you're feeling generous today thank you!
    6·1 answer
  • The total change 6 practical is -48 unit. All the practical have the same charger what is the charge on each particle?
    5·1 answer
  • the perimeter of a 5-sided figure is 45.56 meters two of the sides have the same length. the sum of the other three side lengths
    12·2 answers
  • Carlos's father bought him a 18-foot board to cut into shelves for his bedroom. Carlos plans to cut the board into 7 equal size
    14·1 answer
  • What is the sequence of the function why equals 4X -3
    6·1 answer
  • Which expression is equivalent to 1/3y
    13·2 answers
  • The following question find the value of the variables. If your answer is not an integer leave it in simplest radical form
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!