Question

高数问题求解答 急

Matematics II
1. Given
f(x; y) = x3 􀀀 y3 􀀀 2xy + 6
nd its critical points, and determine if they are relative extremums or
saddle points.
2. Given
f(x; y; z) = exy + xz 􀀀 1
and the point P = (1; 0; 1), nd:
(a) the gradient of f at P
(b) the directional derivative of f along the direction (1;􀀀1; 2)
(c) the direction of maximal slope of f at P
(d) the slope of f along this direction
3. We are given the equation
x3 + 2y3 + z3 = 3xyz + 2y 􀀀 5x + 1:
(a) Show that it denes a function z = z(x; y) around (0; 0; 1).
(b) Find the partial derivatives of the implicit function z at (0; 0).
(c) Find the tangent plane to z(x; y) at the same point.

Answer 1

如图所示：