Section 14.8: Lagrange Multipliers
Exercise 45
The plane \(x + y + 2z = 2\) intersects the paraboloid \(z = x^2 + y^2\). Find the points on this ellipse that are nearest to and farthest from the origin.
The plane \(x + y + 2z = 2\) intersects the paraboloid \(z = x^2 + y^2\). Find the points on this ellipse that are nearest to and farthest from the origin.