IDZ 10.2 - Option 29. 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)
1.29 S: z = x2 + 2y2 + 4xy - 5y - 10, M0 (-7, 1, 8)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.29 z = ln (3xy - 4)

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

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