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Consider the function $z(x,y)$ describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?

 Dec 3, 2020
 #1
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No clue about this one....but...it looks interesting   !!!!!

 

 

cool cool cool

 Dec 3, 2020
 #2
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Hehe it's fine

 Dec 3, 2020
 #3
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Archimedes should choose x = 1/4.

 Dec 3, 2020

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