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Domain and Lagrange multipliers

1. State the largest possible domain for the definition of the function.
f(x,y) = cube-root(y^2-x)

2.The plane 2y+4z = 5 meets the cone z^2 = 4(x^2+y^2) in a curve. Use the method of Lagrange multipliers to find the point on this curve nearest to the origin.

Solution Summary

This shows how to determine a domain and use Lagrange multipliers to find a point on a curve nearest the origin.