IDZ 10.2 - Option 15. 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)
1.15 S: 4y2 - z2 + 4xy - xz + 3z = 9, M0 (1, -2, 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.15 z = sin√x3y

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

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.15 z = x2 - 2xy - y2 + 4x + 1, D: x = -3, y = 0, x + y + 1 = 0