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# Week9extra - ECON 117 Mathematical Economics Spring 2008...

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ECON 117 Spring 2008 Mathematical Economics III. Mathematical Programming 1. Maximization and Minimization without Constraint 1.1 One variable case: : f \\ ( f is continuous and continuously differentiable) Q) Find all local max points and a global max point. Def) () f x has a local max at 0 x iff 00 ( ) ( ) small 0 fx fx h h >+∀ f x has a global max at 0 x iff ( ) ( 0 h Page 1 of 3

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ECON 117 Spring 2008 Mathematical Economics Theorem) By Taylor’s expansion of () f x at 0 x up to the order, we have th n () 2 00 0 0 0 ( ) 1! 2! ! n n n fx f x f xf x x x x x x x R n ′′ =+ + + + + " Then, between R x and 0 x such that (1 ) 1 0 ) ! n n n fR Rx n + x + =− + Theorem) f x has a local max at
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Week9extra - ECON 117 Mathematical Economics Spring 2008...

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