IDZ 10.2 - Option 25. 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)
1.25 S: 2x2 - y2 + z2 - 6x + 2y + 6 = 0, M0 (1, -1, 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.25 z = cos (3x2 - y3)

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

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.25 z = 6xy - 9x2 - 9y2 + 4x + 4y, D: x = 0, x = 1, y = 0, y = 2