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
nalin [4]
2 years ago
13

A continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−5 f(x) has a local minimum

at x=−2 f(x) has a local maximum at x=2
Computers and Technology
1 answer:
butalik [34]2 years ago
7 0

The continuous and differentiable function where f(x) is decreasing at x = −5 f(x) has a local minimum at x = −2 f(x) has a local maximum at x = 2 is given as: y = 9x - (1/3)x³ + 3.

<h3>What is a continuous and differentiable function?</h3>

The continuous function differs from the differentiable function in that the curve obtained is a single unbroken curve in the continuous function.

In contrast, if a function has a derivative, it is said to be differentiable.

<h3>What is the solution to the problem above?</h3>

It is important to note that a function is differentiable when x is set to a if the function is continuous when x = a.

Given the parameters, we state that

f'(5) < 0; and

x = -5

The local minimum is given as:
x = -3;

the local maximum is given as

x = 3

Thus, x = -3 ; alternatively,

x = 3.  With this scenario, we can equate both to zero.

Hence,

x + 3 = 0;

3-x = 0.

To get y' we must multiply both equations to get:

y' = (3-x)(x + 3)

y'   = 3x + 9 - x² - 3x

Collect like terms to derive:

y' = 3x - 3x + 9 - x²; thus

y' = 9-x²

When y' is integrated, the result is

y = 9x - (x³/3) + c

Recall that

F (-5) < 0

This means that:

9 x -5 - (-5³/3) + c < 0
⇒ -45 + 125/3 + c <0
⇒ -10/3 + c < 0

Collecting like terms we have:
c < 10/3; and

c < 3.33


Substituting C into

f(x) = 9x - x³/3 + c; we have

f(x) = 9x - x³/3 + 3, which is the same as  y = 9x - (1/3)x³ + 3.

Learn more about differentiable functions at:
brainly.com/question/15047295
#SPJ1

You might be interested in
What is the answer ??​
Natali5045456 [20]

<em>=</em><em> </em><em>Option</em><em> </em><em>b</em><em> </em><em>Minicomputer ..........</em>

3 0
2 years ago
Read 2 more answers
Which of these might be an example of an advertisers target group
Eduardwww [97]
Where are the examples?

3 0
3 years ago
To keep you from inadvertently moving controls as you work in the IDE, click the form or control, then click the _________ optio
Alenkinab [10]

Answer:

Lock controls

Explanation:

4 0
3 years ago
Copyrighted software illegally downloaded and sold by organized groups without a license to do so is called:
trasher [3.6K]
Copyrighted software illegally downloaded and sold by organized groups without a license is called Warez
5 0
3 years ago
What type of software can you use to capture and examine the contents of network messages?
Ludmilka [50]
They're usually referred to as packet sniffers.
7 0
3 years ago
Other questions:
  • A dropped packet is often referred to as a _____________.
    7·1 answer
  • We will pass you 2 inputsan list of numbersa number, N, to look forYour job is to loop through the list and find the number spec
    12·1 answer
  • Which are appropriate uses for special effects in presentations?
    14·1 answer
  • What is industry 4.0 -automation revolution-, what is your opinion about the direction this revolution is taking the industry in
    8·1 answer
  • What could be one rule to help your friend to blog safely
    6·2 answers
  • E-What is the important of Recycle bin?<br>Ans:​
    12·1 answer
  • What do you hope will be in/added GTA 6?
    13·1 answer
  • Which group scope can be used to assign permissions to resources only in the domain in which the group is created
    12·1 answer
  • 7. Explain the steps for formatting a shape ?
    5·1 answer
  • Someone put malware on your computer that records all of your keystrokes. what aspect of security was primarily attacked? choose
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!