Consider the function f(z, y) kr? -2zy +y?. %3D 1. Show that (0, 0) is a critical point of f(z, y). 2. Determine the values of k (if any) for which the critical point at (0, 0) would be each of the...

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Extracted text: Consider the function f(z, y) kr? -2zy +y?. %3D 1. Show that (0, 0) is a critical point of f(z, y). 2. Determine the values of k (if any) for which the critical point at (0, 0) would be each of the following: i. A local maximum ii. A local minimum iii A saddle point iv Unclassifiable (the second derivative test is inconclusive)