# QUIZ-8-Answer - QUIZ#8 ENGR 3723 PROBLEM 1 Consider f x = 3...

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QUIZ #8 ENGR 3723 PROBLEM 1 Consider ) 2 3 cos( * 3 ) ( = x x f A) (10 points) Find the maximum analytically ANSWER: 3 / 2 0 2 3 0 ) 2 3 sin( * 9 ) ( ' = = = = x x x x f Maximum x f x f x x f < = = = 0 ) ( " 27 ) 0 cos( * 27 ) ( " ) 2 3 cos( * 27 ) ( " B) (35 points) Find the maximum using Newton Raphson. Start from x=0. ANSWER: Actually, if one starts from x=0, one converges to a minimum ) ( " / ) ( ' 1 i i i i x f x f x x = + xi f ' (xi) f " (xi) 0 8.183677 11.23596 -0.72835 -7.7773 13.5876 -0.15596 5.61493 21.10102 -0.42206 -1.11844 26.7907 -0.38031 0.005839 26.99999 -0.38053 -8.2E-10 27 -0.38053 1.1E-15 27 -0.38053 1.1E-15 27 If one starts from x=1, one converges to a maximum. xi f ' (xi) f " (xi) 1 -7.57324 -14.5882 0.480864 4.760893 -22.913 0.688645 -0.593 -26.9413 0.666635 0.000861 -27 0.666667 -2.6E-12 -27 0.666667 0 -27 0.666667 0 -27 0.666667 0 -27

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C) (55 points) Find the maximum using Golden Search. Use 0 and 1 as starting points. ANSWER:
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## This note was uploaded on 08/31/2011 for the course ENGR 3723 taught by Professor Staff during the Summer '11 term at Oklahoma State.

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QUIZ-8-Answer - QUIZ#8 ENGR 3723 PROBLEM 1 Consider f x = 3...

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