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EXAMPLE 3 Using Lagrange Multipliers Find the maximum and minimum values of z = f ( x , y ) = 3 x - y

EXAMPLE

3

Using Lagrange Multipliers

Find the maximum and minimum values of

z = f (x, y) = 3 x - y + 1

subject to the constraint

3 x^{2} + y^{2} = 9 .

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