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319handout1

# 319handout1 - Econ 319 Fall 2008 TA Simon Kwok Handout 1...

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Econ 319, Fall 2008 TA: Simon Kwok Handout 1 Di/erentiation: 1. Compute the derivatives y 0 . (a) y = 3 x 7 + 5 x (b) y = x 2 ° 8 x + 4 (c) y = (3 x 7 + 5 x )( x 2 ° 8 x + 4) (d) y = 3 x 7 +5 x x 2 ° 8 x +4 (e) y = (3 x 7 + 5 x ) 10 (f) y = x p x 2 ° 8 x +4 (g) y = e x 2 ° 8 x +4 (h) y = ln( x 2 ° 8 x + 4) (i) y = ln ln x (j) y = e e x (k) y = sin(3 x 7 + 5 x ) 2.(a) Compute the °rst two derivatives of f ( x ) = 1 p 2 ° e ° ( x ° 1) 2 2 . (b) Where is the maximum of f ( x ) attained? 3. We want to °nd the value of ° that maximizes g ( ° ) = 1 p 2 ° e ° (1 ° ° ) 2 2 ± 1 p 2 ° e ° (3 ° ° ) 2 2 ± 1 p 2 ° e ° (5 ° ° ) 2 2 . (a) First obtain the expression L ( ° ) = ln g ( ° ) . (b) Show that L ( ° ) is an increasing function of g ( ° ) . (c) Find the value of ° that maximizes g ( ° ) . Integration:

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319handout1 - Econ 319 Fall 2008 TA Simon Kwok Handout 1...

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