IDZ 10.2 - Option 30. 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)
1.30 S: z = 2x2 - 3y2 + xy + 3x + 1, M0 (1, -1, 2)

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

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.30 z = 2 (x + y) - x2 - y2

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.30 z = 2x2y - x3y - x2y2, D: x = 0, y = 0, x + y = 6