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.

Name: 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.
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The Answer of 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.

Let f(x,y)=kx3−3kx+y2f ( x , y ) = k x ^ { 3 } - 3 k x + y ^ { 2 }f(x,y)=kx3−3kx+y2

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