SOLUTION: Find the absolute extrema of
f(x)=x^a(1-x)^b
where 0</= x =/< 1 and a and b are constants, both >1
I have the derivative
f'(x)=ax^(a-1)(1-x)^b-x^(a)b(1-x)^(b-1)
Unsure o
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-> SOLUTION: Find the absolute extrema of
f(x)=x^a(1-x)^b
where 0</= x =/< 1 and a and b are constants, both >1
I have the derivative
f'(x)=ax^(a-1)(1-x)^b-x^(a)b(1-x)^(b-1)
Unsure o
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Question 1024797: Find the absolute extrema of
f(x)=x^a(1-x)^b
where 01
I have the derivative
f'(x)=ax^(a-1)(1-x)^b-x^(a)b(1-x)^(b-1)
Unsure of where to go from this point. Thank you for the help Answer by ikleyn(53765) (Show Source):
You can put this solution on YOUR website! .
Find the absolute extrema of
f(x)=x^a(1-x)^b
where 01
I have the derivative
f'(x)=ax^(a-1)(1-x)^b-x^(a)b(1-x)^(b-1)
Unsure of where to go from this point. Thank you for the help
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Next step is to write an equation f'(x) = 0, which gives you this:
= . (1)
Now cancel both sides of (1) by the factor . You will get
a*(1-x) = b*x.
a - ax = bx
a = (a+b)*x,
x = . 1-x = .
f(x) = .
