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

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) = .

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