( The discriminant fxx fyy-fy 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. Be sure that you can explain your reasoning! f(x, y) = x¹y4 The critical point at the origin is ✓? f(x, y) = 1- x¹y4 The critical point at the origin is a local maximum a local minimum neither a local maximum nor a local minimum f(x, y) = xy4 The critical point at the origin is: ? f(x, y) = x³y4 The critical point at the origin is: ? f(x, y) = x³y³ The critical point at the origin is: ? f(x, y) = x¹y6 The critical point at the origin is: ? + +

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