IDZ 10.2 - Option 5. 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)
1.5 S: 2x2 - y2 + z2 - 4z + y = 13, M0 (2, 1, - 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.5 z = sin (x2 - y)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.5 z = x3 + y2 - 6xy - 39x + 18y +20

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