HMMT - Februrary 2015 - GUTS!

Calculus Level 5

Consider the function z ( x , y ) z(x, y) describing the paraboloid z = ( 2 x − y ) 2 − 2 y 2 − 3 y z = (2x - y)^2 -2y ^2 - 3y .

Archimedes and Brahmagupta are playing a game. Archimedes first chooses x x . Afterwards, Brahmagupta chooses y y . Archimedes wishes to minimize z z while Brahmagupta wishes to maximize z z . Assuming that Brahmagupta will play optimally, what value of x x should Archimedes choose?


The answer is -0.375.

Alisa Meier by Alisa Meier , 24, Germany

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1 solution

Bob Kadylo
Sep 17, 2018

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