IDZ 10.2 - Option 23. 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)
1.23 S: x2 - y2 - 2z2 - 2y = 0, M0 (-1, -1, 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.23 z = arccos (x - 5y)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.23 z = x2 - xy + y2 + 9x - 6y + 20

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
4 5.23 z = (x - y) - x2 - y2, D: x + 2y = 4, x - 2y = 4, x = 0