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# Week2 - ECON 117 Mathematical Economics Spring 2008 Week 2...

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ECON 117 Spring 2008 Mathematical Economics Week 2 3.2 Differentiation of a Real Function Def) Real function : : f XY is a real function if Y \ Q) Draw the following real function: (1) 2 282 f xx =− + (2) 22 yx = + Def) Differentiation of a real function Page 1 of 10

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ECON 117 Spring 2008 Mathematical Economics Q) Find () f x of the following functions (1) () 3 f xx = (2) () 3 fx = Q) ( Addition Rule ) Show that if () yf xg x = + , then x ′′ = + . Q) Show that if , then 3 yx = 2 3 ′ = Page 2 of 10
ECON 117 Spring 2008 Mathematical Economics Q) ( Product Rule ) Show that if () () yf xg x = , then x g xf x g x ′′ = ⋅+⋅ Q) ( Chain Rule ) Show that if (() ) g x = , then ) () g x g x = Q) ( Quotient Rule ) Show that if () f x y gx = , then 2 [() ] f xgx fxgx y −⋅ ′ = Page 3 of 10

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ECON 117 Spring 2008 Mathematical Economics 3.3 Approximation of a Real Function Q) Find 00 () ( ) 0 f xf x x x +⋅ in the above diagram Page 4 of 10
ECON 117 Spring 2008 Mathematical Economics Q) Prove the Taylor’s expansion.

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Week2 - ECON 117 Mathematical Economics Spring 2008 Week 2...

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