Theory and ExamplesThe discriminant is zero at the origin

Chapter 14, Problem 44E

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Problem 44E

Theory and Examples

The discriminant is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a maximum, a minimum, or neither at the origin by imagining what the surface z = f(x,y) looks like. Describe your reasoning in each case.

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