Given:

Multivariable functionf(x,y)=ky²- 2y³-kx³+ 2kxy

A.The function f(x,y)has a critical point at (0,0). Use the second derivative test to demonstrate that for all nonzero values ofk, fhas a saddle point at (0,0). Use algebra and/or calculus techniques to justify all work.

B.The function f(x,y)has a critical point at (-1/3,1/6). Use the second derivative test to demonstrate that for k = -1/2, fhas local maximum at (-1/3,1/6). Use algebra and/or calculus techniques to justify all work.