IDZ 10.2 - Option 7. 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)
1.7 S: x2 + z2 - 5yz + 3y = 46, M0 (1, 2 - 3)

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

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.7 z = 3x3 + 3y3 - 9xy + 10

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.7 z = 2x3 - xy2 + y2, D: x = 0, x = 1, y = 0, y = 6