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
Create a equation to solve for the mid segment with bases x-6 and 2x-9
Readme [11.4K]

Answer:

Step-by-step explanation:

If AD=DB  and  AE=EC,

then DE¯¯¯¯¯∥BC¯¯¯¯¯ and DE=12BC .

8 0
2 years ago
A grocery store sells snacks by weight. A 6-oz bag of gummy worms costs $3.60. How much would it cost for a 2-oz bag?
Whitepunk [10]

Answer:

$1.20

Step-by-step explanation:

3 0
2 years ago
Help on 2 pleeeeeaaassseee
Anastasy [175]
10^9 (Ten to the power of nine)
5 0
2 years ago
So I have another math question that involves the same problem and so is 7 + 7x the same as 7x+ 7 i think it is but i'm not sure
BartSMP [9]

Answer:

it is

Step-by-step explanation:

because it addition it doesn't matter which way you put it

6 0
1 year ago
Read 2 more answers
Helpppppp 50 pointssss
djyliett [7]

Answer:

A

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Other questions:
  • Complete this statement 27x^4a^2+18x^2a^3=9x^2a^2 ( )
    5·1 answer
  • the average sunflower has 34 petals. which is the best estimate of the total number of petals on 57 sunflowers
    15·1 answer
  • What decimal is equivalent to 80/100
    7·1 answer
  • 1.      Solve for s.<br><br>Rs + t = u
    11·1 answer
  • HELP PLEASE
    12·1 answer
  • 1] A triangle with sides of 8, 15, and 16 is a right triangle.
    13·1 answer
  • I NEED HELP ASAP WILL MARK BRAINLIST. NOTE: EVERYTHING IS ALREADY ANSWERD ALL I NEED HELP WITH IS QUESTION 8 AND 9 PLEASE
    12·2 answers
  • A man and his three children spent $40 to attend a show. A second family of three children and their two parents spent $53 for t
    8·1 answer
  • [ tan2 θ ] – [( sec θ – 1 )( sec θ + 1 )
    15·1 answer
  • Rút gọn biểu thức √81a^6b^2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!