Really need your help on some multivariable calculus

HTale

New member
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Dec 17, 2008
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Hi there guys, i'm having alot of trouble verifying the following i don't know where to begin!

verify the maximum of

x(1x)y(1y)w(1w)(1(1xy)w)1\displaystyle \displaystyle x(1-x)y(1-y)w(1-w)(1-(1-xy)w)^{-1}

occurs for x=y\displaystyle x=y and then that

x(1x)y(1y)w(1w)(1(1xy)w)(21)4\displaystyle \displaystyle \frac{x(1-x)y(1-y)w(1-w)}{(1-(1-xy)w)} \leq (\sqrt 2 - 1)^4

thanks alot in advance
 
HTale said:
Hi there guys, i'm having alot of trouble verifying the following i don't know where to begin!

verify the maximum of

x(1x)y(1y)w(1w)(1(1xy)w)1\displaystyle \displaystyle x(1-x)y(1-y)w(1-w)(1-(1-xy)w)^{-1}

occurs for x=y\displaystyle x=y and then that

x(1x)y(1y)w(1w)(1(1xy)w)(21)4\displaystyle \displaystyle \frac{x(1-x)y(1-y)w(1-w)}{(1-(1-xy)w)} \leq (\sqrt 2 - 1)^4

thanks alot in advance

What is the condition for maximum of a multi-variate function?

Please show us your work, indicating where your stuck - so that we know where to begin to help you.
 
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