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In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4...

Question:

In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4 g
12.) Use the method of Lagrange multipliers to minimize f(x, y) = x² + y² subject to the constraint equation - 3x + g = 30 (Y
In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4 g
12.) Use the method of Lagrange multipliers to minimize f(x, y) = x² + y² subject to the constraint equation - 3x + g = 30 (You do NOT have to verify that it is a minimum.

Answers

11) flogy) = 2012 40ytt ye OF 48-49 By -4x+41443) =-40+y3 Now af ax af dy 45-45=0, -48493=0. 4X=44 y3 = 45€. - x=y la SubstitAt 10,0) In.m² = 12 (0)²-16 = 0-16=-1620 The point (0,0) is a saddle Point. At (22) In-m²= 12/2)²-16=12 (4)-16 = 48-16 = 3230DF - 2x+ d(-3) ax a F -2y+d() ay • Now a 70 OF ay 2x-32=0, 297d=0 ,darzy 30=2x d = 2 x - d=-24 from @ f 0 x=-24 2x=-69 => y =

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