Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject to the constraint. w = 2x² + 6y² + 2z² + 4xy + 4xz + 4yz; x² + y² + z² = 1 The constrained maximum of (x, y, z) = occurs when (x, y, z) = and the constrained minimum of occurs when

3 Find the least squares cubic equation that best fits the points: (-2,-2), (-1, 1), (0, 1), (1, 2), (2, 2).

Determine the point in which the following line:

The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional space, is a3 – 13 – 4x1x2 – 4x1x3 = 1. Identify the type of surface, and find the least distance from a point on the surface to the origin.