Really need your help on some multivariable calculus

[HTale]

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

verify the maximum of

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

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

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

thanks alot in advance

 

[Deleted member 4993]

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

verify the maximum of

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

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

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

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.