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An Unusual Critical Point Consider the function fiery} = (y? - $3M? - 233}- 1. Establish that (0,0) is a critical point for 3'. Does f have any other critical points? 2. Show that the second-order partial derivative test fails to establish whether I has a local maximum, local minimum, or a saddle point at this critical point. 3. Examine the behavior of at, y) along every line in the ey-plane passing through the origin. Does anything special happen there? 4. What does 1' have at the origin, a maxmum, a minimum1| or a saddle point? Hint: Where is f positive, where is f negative, and where is f equal to 0? 5. Explain intuitively what is going on. Explain what is strange here and how to reconscile it. Graph f in threedimensions, and explain in words what the graph looks like