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GreenHerbz206
05.02.2020 •
Mathematics
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.
your answer may depend on a and b. what is the maximum value?
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Ответ:
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.
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Ответ:
One
Step-by-step explanation: