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
Setler [38]
2 years ago
9

If a and b are positive numbers, find the maximum value of f(x)=x^a*(1-x)^b, 0 less than or equal to x less than or equal to 1.

Mathematics
1 answer:
Pavel [41]2 years ago
7 0
 <span>f '(x) = ax^(a-1)(1 - x)^b - bx^a (1 - x)^(b-1) = x^(a-1)(1 - x)^(b-1) (a(1 - x) - bx). 


If a < 1 or b < 1, this may not be defined at one or both of the end points. f '(x) = 0 if the right most term is zero. 


a - ax - bx = 0 ==> x = a/(a + b). 


Note that this number is both well define and is between 0 and 1. 


f(0) = 0 

f(1) = 0, 

f(a/(a+b)) = a^ab^b/(a + b)^(a + b) <--- the maximum value.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

</span>
You might be interested in
Find the surface area of a square prism with a side measure of 15
Phoenix [80]
Since the length is 15, and the width would be 15, you need to first do 15 x 15.

15 x 15 = 225


Multiply the 6 faces.

225x6

Your final answer would be 1,350.
7 0
3 years ago
Joanie watched 1 out of three of a movie in the morning
Archy [21]

Answer:

7/15

Step-by-step explanation:

Determine how much she has watched.

1/3 + 1/5 The common denominator of 3 and 5 is 15. Multiply each fraction by an amount that will make the denominator 15

1/3 = 1*5/(3*5) = 5 / 15

1/5 = 1*3 / (5*3) = 3/15

Now add the two fractions together.

5/15 + 3/15 = 8/15

What is left of the movie? The whole movie = 1 so that which is left is

1 - 8/15

15/15 - 8/15

7 / 15

She has just a bit under 1/2 to go.

8 0
3 years ago
What is a rational number
dsp73
Anything except pi is a rational number. So 9 and 7/10 is one or it could be a whole number
7 0
3 years ago
Higher Order Thinking What is the<br>least multiple 6 and 8 have in common?<br>Explain.​
Dahasolnce [82]

Answer: 24

Step-by-step explanation:

6, 12, 18, 24

8, 16, 24

3 0
3 years ago
Read 2 more answers
Which mathematical property is demonstrated?
Orlov [11]
Commutative property of multiplication is shown above. This is because no matter how you put them, the answer will still be 140. 
5 0
2 years ago
Other questions:
  • Which value of x satisfies both -9x+4y=8 and -3y-y=4
    8·1 answer
  • 168÷7= find the distributive property
    11·1 answer
  • Can someone plz help me?
    8·1 answer
  • Will give 32 points! Read the excerpt from act 1 of The Monsters Are Due on Maple Street.
    11·1 answer
  • Determine whether the lines are parallel.<br> A.yes<br> B.no
    6·2 answers
  • I am not sure of the answer on this one.
    11·2 answers
  • Find the area of the triangle.<br> A) 78 m2 <br> B) 175 m2 <br> C) 196 m2 <br> D) 350 m2
    6·2 answers
  • PLEASE HELP BRAINIEST!❤️
    6·1 answer
  • In about how many seconds could a 9-year old boy run 100 meters?
    7·1 answer
  • Estimate, then add. Write each sum in the simplest form.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!