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# ANAL GEO & CALCULUS MATH 016B

GPA 3.93

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This 2 page Class Notes was uploaded by Kavon Feest on Thursday October 22, 2015. The Class Notes belongs to MATH 016B at University of California - Berkeley taught by T. Scanlon in Fall. Since its upload, it has received 33 views. For similar materials see /class/226587/math-016b-university-of-california-berkeley in Mathematics (M) at University of California - Berkeley.

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Date Created: 10/22/15

SOLUTIONS TO SPRING 2008 MIDTERM 1 FOR MATH 16B 1 i 2 tzu 4 lnu3st Fstu is 6 3 S2es 8F 7 2 2 21 3112 Bu it 3 e l u3sts2es hence 62F 2g Buat 7 at Bu 7 2 2t 2 tzu 273 2 Ru 7 5 s e us 6 us St282 65 2 Using the method of Lagranage multipliers the associated function is Hzyz z23y222 721 7 5y74210M312y427 15 Taking each partial derivative and setting the results equal to zero we have 0 E 21 7 2 3A 81 0 8H 6y752 19y 8H 0 7 22 7 4 4A 82 8H 0 a 312y42715 Combining the rst two equations eliminating A we nd I 7 9 E 7 2y 4 The second two equations yield 2 6y 7 3 Substituting into the last equation we have 9 g 2 y 7 4 or g y 7 158 Thus E I 7 79 and 186 Z 7 79 1 2 SOLUTIONS TO SPRING 2008 MIDTERM 1 FOR MATH 15B 3 The sum of squares of errors for f is 7 12 3 7 22 7 33 15 while the sum of squares of errors for g is 71 7 l2 2 7 22 3 7 33 4 Thus f is a closer t based on the least squares method 4 Fzy 2y6173217y2475 hence 8F 2 E 7 32 BI ye 8F 7 2 T 7 2 By E y Setting these equal to zero using 0 we nd y 6 Substituting into the rst equation we nd 262 32 Dividing by 2 and taking natural logarithms we nd I ln4 and thus y 4 Computing second derivatives 261 Bray 7 Hence the Hessian is DF 74yex 7 4627 So that at the one potential relative extremum or saddle point we have DF ln4 4 7128 lt 0 Hence this point is a saddle point 5 a ADF b H c B d K e l

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