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jmc

algebra senior

Problem

Consider the function describing the paraboloid Archimedes and Brahmagupta are playing a game. Archimedes first chooses Afterwards, Brahmagupta chooses Archimedes wishes to minimize while Brahmagupta wishes to maximize Assuming that Brahmagupta will play optimally, what value of should Archimedes choose?
Solution
Expanding we get After Archimedes chooses Brahmagupta will choose in order to maximize Then To minimize this expression, Archimedes should choose
Final answer
-\frac{3}{8}