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Setler [38]
3 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]3 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!

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Answer:

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Step-by-step explanation:

<u>Step 1:  Find the square root</u>

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3 years ago
What is the relationship between the following two sequences?
LuckyWell [14K]

Answer:

The 1st option

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4 0
3 years ago
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Urgent. There are 12 coloured counters in a bag. The counters are black, white or grey A counter is chosen at random. The probab
Nastasia [14]

Answer:

1/12

Step-by-step explanation:

<u>Needed information</u>

\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}

The sum of the probabilities of all outcomes must equal 1

<u>Solution</u>

We are told that the probability that the counter is <em>not</em> black is 3/4.  

As the sum of the probabilities of all outcomes <u>must equal 1</u>, we can work out the probability that the counter <em>is </em>black by subtracting 3/4 from 1:

\sf P(counter\:not\:black)=\dfrac34

\implies \sf P(counter\:black)=1-\dfrac34=\dfrac14

We are told that the probability that the counter is <em>not </em>white is 2/3.  

As the sum of the probabilities of all outcomes <u>must equal 1</u>, we can work out the probability that the counter <em>is </em>white by subtracting 2/3 from 1:

\sf P(counter\:not\:white)=\dfrac23

\implies \sf P(counter\:white)=1-\dfrac23=\dfrac13

We are told that there are black, white and grey counters in the bag.  We also know that the sum of the probabilities of all outcomes must equal 1.  Therefore, we can work out the probability the counter is grey by subtracting the probability the counter is black and the probability the counter is white from 1:

\begin{aligned}\sf P(counter\:grey) & = \sf1-P(counter\:black)-P(counter\:white)\\\\ & =\sf 1-\dfrac14-\dfrac13\\\\ & = \sf \dfrac{12}{12}-\dfrac{3}{12}-\dfrac{4}{12}\\\\ & = \sf \dfrac{12-3-4}{12}\\\\ & = \sf \dfrac{5}{12}\end{aligned}

7 0
2 years ago
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I believe the answer is A 3^7
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