CHEM 151A Final: Chem 151A UCSC Exam Final 2012
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You have 60 minutes to answer all four questions. Let : r3 r be de ned by. ( ) = 2 + + : show that there exists a di erentiable function in some neighborhood of (1 1) in. ( ( ) ) = 0: compute (1 1). Suppose : r r is maximized globally at and that : r r is an increasing function (that is, ( ) ( ) whenever ). Prove that is the global maximizer of the function : r r where = (that is, ( ) = ( ( )) for all ). Prove that if is convex and x is a local minimizer of , then x is a global minimizer.
