IDZ 10.2 - Option 1. 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)
1.1 S: x2 + y2 + z2 + 6z - 4x + 8 = 0, M0 (2, 1, - 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.1 z = ex2-y2
 
3. To verify whether the above equation the function u.

4. Examine the following function extremum.
4.1 z = y√x - 2y2 - x + 14y

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