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
aleksandrvk [35]
3 years ago
14

Suppose f is a differentiable function such that f′(x)≤2 for all x∈[1,3]. If f(1)=4, the Mean Value Theorem says that f(3)≤V for

what value of V? (Choose V as small as possible.)
Mathematics
1 answer:
Pavel [41]3 years ago
7 0

The MVT guarantees the existence of c\in(1,3) such that

f(c)=\dfrac{f(3)-f(1)}{3-1}=\dfrac{f(3)-4}2

Since f'(x)\le2 for all x\in[1,3], we have

\dfrac{f(3)-4}2\le2\implies f(3)-4\le4\implies f(3)\le8

so that V=8.

You might be interested in
PLEASE HELP ME! Tysm <3 Have a great day. The Picture is below.
kykrilka [37]

Answer:

1.false

2.false

3.false

7 0
3 years ago
Read 2 more answers
I need help! Someone help me please
liberstina [14]

Answer:

4. 27

Step-by-step explanation:

11-10=1 which is <=16

15-10=5 which is <=16

26-10=16 which is <=16

27-10=17 which isn't <=16

Therefore 27 doesn't satisfy the inequality

4 0
3 years ago
Read 2 more answers
Find the exact value of tan 15 degrees
pentagon [3]
<span>tan(15) = 
sin(15) / cos(15) = 
sin(45 - 30) / cos(45 - 30) = 
[ sin(45)cos(30) - sin(30)cos(45) ] / [ cos(45)cos(30) + sin(45)sin(30)] 

Since sin(45) = cos(45) = √2/2, you can just factor that out from the top and bottom 
[ cos(30) - sin(30) ] / [ cos(30) + sin(30)] 
[ √3/2 - 1/2 ] / [ √3/2 + 1/2] 
(√3 - 1) / (√3 + 1) 
(√3 - 1)^2 / (√3+1)(√3 - 1) 
(√3 - 1)^2 / (3 - 1) 
(3 - 2√3 +1) / 2 
2 - √3 

There's also a formula for tan(a-b), but I couldn't remember it off hand.</span>
4 0
3 years ago
Find a positive angle less than one rotation that is coterminal with –308°.
Anna35 [415]
The answer would be -72 cuz -308 + -72 is -360 which is a whole circle


warningggg: if this is a home quiz your taking , don't put my answer down cuz there is a 30% chance my answer is wrongdoing
5 0
3 years ago
Read 2 more answers
Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C.
valentina_108 [34]

Answer:

<em>Correct answer:</em>

<em>A. I and II</em>

<em></em>

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with f^{-1}(x)

Given that:

I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = a^{-1}(x) = a(x)  Hence, I is true.

II. y =\dfrac{1}{x}

Replacing y with and x with y:

x =\dfrac{1}{y}

x=\dfrac{1}{a^{-1}(x)}

\Rightarrow a^{-1}(x) = \dfrac{1}{x}

a^{-1}(x) = a(x)  Hence, II is true.

III. y =x^{2}

Replacing y with and x with y:

x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)

 Hence, III is not true.

IV. y =x^{3}

Replacing y with and x with y:

x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)

Hence, IV is not true.

<em>Correct answer:</em>

<em>A. I and II</em>

<em></em>

4 0
3 years ago
Other questions:
  • Jamal has been approved for $125,000 loan, 30-year mortgage with an APR of 5.3%. He made a 10% down payment and is closing on Ap
    5·2 answers
  • how much would $100 invested at 6% interest compounded monthly be worth after 20 years? Round your answer to the nearest cent a(
    14·1 answer
  • Oliver needs to save at least $1500 to buy a computer. he already has saved $650. how solve the inequality
    13·2 answers
  • How do you do 2 step eqations
    13·1 answer
  • Use the zero product property to find the solutions to the equation x^2-15x-100=0
    11·1 answer
  • Combine the like terms to create an equivalent expression:<br> -3r- 6+ (-1)
    11·2 answers
  • I need help with my homework please, I don’t understand
    8·1 answer
  • Solve 5|x – 4| ≥ –10
    8·1 answer
  • How are you really? 100 points, Be honest.
    6·2 answers
  • Find the Area of a square tablecloth with 42.5-inch sides.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!