Find all local maxima, local minima, and saddle points of f(x, y) = x^3 - 3x^2 +

Question

Find all local maxima, local minima, and saddle points of f(x, y) = x^3 - 3x^2 + 2y^2 -12y + 8 Find the parametric equations for the plane tangent to the surface z = x^2 + 4y^2 at the given point (1, 1, 5) Consider the following Lagrange Multipliers problem: Find the point closest to the point (6, -7, 0) on the intersection of the planes x - 2y = 3 and 7x + 6y -2z = 4. Answer the following four questions only - do not solve the problem itself!!! a) Specify the objective function (in the form f(x, y) or f(x, y, z)) b) Specify the constraint(s).

Explanation / Answer

2) At (1,1,5) the equation of tangent is

1/2 (z+5) = x(1) + 4y(1),

Z+5 =2 (x+4y),

2x + 8y - z - 5 =0.

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