Let $f ( x , y ) = k x ^ { 3 } - 3 k x + y ^ { 2 }$

Essay

Let $f ( x , y ) = k x ^ { 3 } - 3 k x + y ^ { 2 }$ where k $\neq$ 0.Determine the values of k (if any)for which the critical point at (-1, 0)is a local minimum.