ABSTRACT
From the one-dimensional theory we know that Proposition 25 does not cover all possibilities. For example f(x) = x4 has a local minimum at the origin but f ′(0) = f ′′(0) = 0, while g(x) = x3 has neither a local maximum nor a local minimum at the origin yet, g′(0) = g′′(0) = 0 (Figure 5.1).
