Find all local maxima local minima and saddle points of fx y

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).

Solution

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.