Exam 2 Key - Spring 2008

# Exam 2 Key - Spring 2008 - MET 581 Optimization Exam 2...

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MET 581 Optimization Exam 2 - Mathcad Exam f 1 x ( ) 200 sin x 10 e x 50 2 1 100 x 2 + 2x + := To make sure you have the equation programmed correctly, here are some sample values f 1 0 () 0 = f 1 10 ( ) 182.695 = f 1 10 ( ) 180.695 = 200 150 100 50 0 50 100 150 200 500 0 500 1000 f 1 x () x Problem 1 - Plot the derivative of f1(x) in the range -100 < x < 100 100 50 0 50 100 20 0 20 40 x f 1 x d d x

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Problem 2 - Find the global minimum and the two local minima. Make sure to identify which is which x0 := Minimize f 1 x , () 15.406 = <= global minimum df 1 x x f 1 x d d 20 cos 1 10 x e 1 2500 x 2 4 25 sin 1 10 x xe 1 2500 x 2 1 50 x + 2 + := d2f 1 x 2 x f 1 x d d 2 54 25 sin 1 10 x e 1 2500 x 2 4 125 cos 1 10 x 1 2500 x 2 2 15625 sin 1 10 x x 2 e 1 2500 x 2 + 1 50 + := Starting Point Make Sure This is a Minimum Find Root x7 0 := x star root df 1 x ()x , := x star 75.179 = d2f 1 x star 0.244 = <= Local x2 0 := x
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Exam 2 Key - Spring 2008 - MET 581 Optimization Exam 2...

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