The given multivariable function is as follows: f(x,y) = ky² - 2y³ - kx³ + 2kxy.

A. Given that the function f(x,y) in the Assumptions section has a critical point at (0,0), use a second derivative test to explain why the function fhas a saddle point at (0,0) for all nonzero values of k. Show your work.

B. Given that the function f(x,y) in the Assumptions section has a critical point at (2/3,2/3) when k= 1, use a second derivative test to determine whether (2/3,2/3) is a local maximum, local minimum, or saddle point, or determine whether a second derivative test is inconclusive. Show your work.