The First and Second Derivative Tests
If the second derivative test fails, then the first derivative test must be used to classify the point in question. Ex. f (x) = x2 has a local minimum at x = 0. Ex. f (x) = x4 has a local minimum at x = 0. But the second derivative test would fail for this function, because f ″(0) = 0. The first derivative test … ................
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