IDZ 10.2 - Option 16. 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)
1.16 S: z = x2 + y2 - 3xy - x + y + 2, M0 (2, 1, 0)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.16 z = arcsin (x - 2y)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.16 z = x√y - x2 - y + 6x + 3

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