IDZ 10.2 - Option 17. 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)
1.17 S: 2x2 - y2 + 2z2 + xy + xz = 3, M0 (1, 2, 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.17 z = arccos (4x - y)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.17 z = 2xy - 5x2 - 3y2 + 2

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