Use lagrange multipliers to find the maximum and minimum

Question

Let f(x,y) = x³ - 12xy + 8y³.

a. Find the following quantities

i. f_x =
ii. f_y =
iii. f_xx =
iv. f_xy =
v. f_yy =

b. Solve f_x = 0, f_y = 0 for critical point (x, y).

c. Use the second derivative test to determine the critical points in (b) are local maximum oi minimum or saddle points.

2. Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z) = 2x + 2y+ z subject to x² + y² +z² = 9.