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Omni-MATH / Consider the function z(x,y) describing the paraboloid z=(2x−y)²−2y²−3y. Archimedes and Brahmagupta are playing a game. Archimedes first chooses x. Afterwards, Brahmagupta chooses …

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problem

Consider the function z(x,y)z(x, y) describing the paraboloid z=(2x−y)2−2y2−3yz=(2 x-y)^{2}-2 y^{2}-3 y. Archimedes and Brahmagupta are playing a game. Archimedes first chooses xx. Afterwards, Brahmagupta chooses yy. Archimedes wishes to minimize zz while Brahmagupta wishes to maximize zz. Assuming that Brahmagupta will play optimally, what value of xx should Archimedes choose?
Plain-text mathematical notation (without MathML)
Consider the function z(x,y) describing the paraboloid z=(2x−y)²−2y²−3y. 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?
Original LaTeX notation
Consider the function $z(x, y)$ describing the paraboloid $z=(2 x-y)^{2}-2 y^{2}-3 y$. 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?

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task_id
d0bf4ced-c85b-5492-b31d-769cda92e4aa
task_key
test--d0bf4ced-c85b-5492-b31d-769cda92e4aa
task_revision_id
1
config / split
/ test

Official source

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