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(Lagrange Multipliers with Three Variables) Find the global minimum value of f(x,y,z)=(x^2/4)+y^2 +(z^2/9) subject to x...

(Lagrange Multipliers with Three Variables) Find the global minimum value of f(x,y,z)=(x^2/4)+y^2 +(z^2/9) subject to x - y + z = 8. Now sketch level surfaces f(x,y,z) = k for k = 0; 1; 4 and the plane x-y +z = 8 on the same set of axes to help you explain why the point you found corresponds to a minimum value and why there will be no maximum value.

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