Use Lagrange multiplier method to find the maximum and minimum values of (, , ) = − 2 + 5 On the sphere 2 + 2 + 2 = 30

Please find the complete question in the attached file.

Step-by-step explanation:

Calculation with Lagrange multipliers of its optimum restricted places,

Set the multiplier formulas for Lagrange:

We get solutions (x,y)=(2,1) and (−2,−1) if combined with 2y = x. These are all the identical points we obtained in (c) and we know the f(2,1) is the max, whereas f(−2, −1) is a minimum.

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step-by-step explanation:

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