MATH 2321 Lecture Notes - Lecture 25: Saddle Point, Fxx, Hessian Matrix

• School: Northeastern University
• Department: Mathematics
• Course: MATH 2321
• Professor: Sumi Seo

Document Summary

X,y)= x3 + 50y2 + x? y. fx = 2x+2xy = 2x(1+y) = 0. 2x=0 ity=0 x=0 or y=-| fy = 100y + x2 = 0, x3 = -1004 case 1: x=0 :. D = 200+ 0-0 >0, fxx = 2+030, local min. => 874-y =0 = y(873-1)=0 y = 0, y3 = 4/8 = (2)}, = : casels y=0. x = 4(0)2 = 03c. p. (0,0, case 2: y=3 x= 4(&) = 15 cp (1,1/2). Dalfxx fxy |_ | 6x -6 l = 6x(484) - (-6) " | fxy fyy | |-6 487 | = 288xy-36. D = 288(1)("/2) -36 = 10870, fxx = 670, local min. D-1 fxx fxy |_ | -6x 0 , D(1,0) = 24 (1-0) = 2410, exx(1,0) = -650 =) local max. D = 24(1)(1-3) to = saddle point: at (1,-1): : d = 24(1-3) to saddle point: at (-1,0): D=-2411-0) <0 = saddle point: at (-1,1):