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13 Nov 2019

a. Find all local extrema for (x, y) = 2y³ + 12x² â 24xy

b. Find the absolute maximum and minimum values of the function f(x, y) = x² + xy + y²

on the disc x² + y² â¤ 1

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Keith LeannonLv2

9 Jun 2019

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Related questions

Consider the function

f(x, y) = x² + xy + y²

defined on the unit disc, namely,

D = {(x, y)| x² + y² ? 1}.

Use the method of Lagrange multipliers to locate the maximum and minimum points for f on the unit circle. Use this to determine the absolute maximum and minimum values for f on D.

Show transcribed image text

a. Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point.

f(x, y) = x² â y² + 3xy

b. Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point.

f(x, y) = x² + y² â xy

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