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
erastovalidia [21]
3 years ago
6

the value of c guaranteed to exist by the Mean Value Theorem for V(x) = x² in the interval [0, 3] is...? a) 1 b) 2 c) 3/2 d) 1/2

e) None of the above
Mathematics
1 answer:
lilavasa [31]3 years ago
4 0

Answer:  c) \dfrac{3}{2} .

Step-by-step explanation:

Mean value theorem : If f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that

\begin{displaymath}f'(c) = \frac{f(b) - f(a)}{b-a} \cdot\end{displaymath}

Given function : f(x) = x^2

Interval : [0,3]

Then, by the mean value theorem, there is at least one number c in the interval (0,3) such that

f'(c)=\dfrac{f(3)-f(0)}{3-0}\\\\=\dfrac{3^2-0^2}{3}=\dfrac{9}{3}\\\\=3

\Rightarrow\ f'(c)=3\ \ \ ...(i)

Since f'(x)=2x

then, at x=c, f'(c)=2c\ \ \ ...(ii)

From (i) and (ii), we have

2c=3\\\\\Rightarrow\ c=\dfrac{3}{2}

Hence, the correct option is c) \dfrac{3}{2} .

You might be interested in
You and a friend are driving go-karts on two different tracks. As you drive on a straight section heading east, your friend pass
yKpoI14uk [10]
No they cross each other like a highway. You are on the underpass and your friend passes over you. As in, they are crossing a bridge & you are below them.
5 0
3 years ago
What is not a solution of -4 &lt; x
Gnesinka [82]

Answer:

-5

Step-by-step explanation:

because it is less than -4 when it is suppose to be more than-4

8 0
3 years ago
Read 2 more answers
What are the factors of 2x + 3x - 54? Select two options
tiny-mole [99]

Answer:

The answer: The factors are (2x-9) and (x+6).

The Problem:

Factor 2x^2+3x-54

Step-by-step explanation:

So I'm going to do trial factors using the choices to aid me.

Factored form for this problem if it exist will be in the form:

(mx+n)(kx+p).

In general this is what it would look like if we factored any quadratic in terms of x (given the quadratic is not prime but technically you could factor even over the complex numbers).

Let's look at:

(mx+n)(kx+p)

We want to choose k \text{ and } m such that when you multiply them you get 2.  Well those would have to be 2 and 1.

(2x+n)(x+p)

we want to choose n \text{ and } p such that when you multiply them you get -54. Based on the choices we want to get with -9 and 6, or 9 and -6. We don't know the order we want to choose it in either.

For example which of these would work:

(2x-6)(x+9)

(2x+6)(x-9)

(2x-9)(x+6)

(2x+9)(x-6)

We are going to consider only the outer and inner of FOIL since we already know the first times the first is 2x^2 and the last times the last is -54.

Let's test the first one:

(2x-6)(x+9)

Outer:  2x(9)=18x

Inner: -6(x)=-6x

------------------------ADD!

18x-6x=12x

The first choice did not give us the middle term 3x.

Trying the second one would give us the opposite since they are in the same form as previous just the + and - are switched.

Let's look at the third one:

(2x-9)(x+6)

Outer: 2x(6)=12x

Inner: -9(x)=-9x

--------------------------ADD!

12x-9x=3x

This is the winner.

The answer: The factors are (2x-9) and (x+6).

7 0
3 years ago
Read 2 more answers
IAN LEAVES NORFOLK VA TRAVELING WEST AT 50MPH ANDREW LEAVES NORFOLK VA 3 HOURS LATER TRAVELS IN THE SAME DIRECTION GOING 68 MPH.
Paladinen [302]
Approximately 5 hours

4 0
3 years ago
Pleasee help me with this i’m being timed
sammy [17]

Answer:

I think she is correct

Step-by-step explanation:

in not. sure so dont take my word for it

4 0
2 years ago
Other questions:
  • If f(x) = 3x + 10x and g(x) = 4x - 2, find (f + g)(x).
    5·2 answers
  • Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and
    13·2 answers
  • Is this equation an identity?<br> 10.95 + 14.5n – 19.73 = 14.5n – 8.78
    15·1 answer
  • Solve the iniquity and graph the solution
    13·1 answer
  • What is the probability of flipping a coin 4 times and it landing heads every time?
    10·1 answer
  • What is 52x /1 = 51x/3
    5·1 answer
  • What is the GCF of 105,30 and 75 and How?
    14·2 answers
  • Write an equation<br> in SIF from the table.<br> X<br> 3<br> -4<br> 2<br> 6<br> 9<br> 8
    6·1 answer
  • Need the answer to this asap pls
    6·2 answers
  • (a) Rearrange the equation<br> x<br> + 2y = 6 to make y the subject.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!