IDZ 10.2 - Option 4. Decisions Ryabushko AP

1. Find the equation of the tangent plane and the normal to the given surface S at the point M0 (x0, y0, z0)
1.4 S: x2 + y2 + z2 + 6y + 4x = 8, M0 (-1, 1, 2)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.4 z = cos (xy2)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.4 z = 1 + 6x - x2 - xy - y2

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.4 z = 5x2 - 3xy + y2, D: x = 0, x = 1, y = 0, y = 1