Initially, second-order necessary optimality conditions and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem $\phi \left(x\right)\to min$, $x\in {ℝ}^m$, are given. These conditions work with arbitrary functions $\phi {ℝ}^m\to \overline{ℝ}$, but they show inconsistency with the classical derivatives. This is a base to pose the question whether the formulated optimality conditions remain true when the “inconsistent” Hadamard derivatives are replaced with the “consistent” Dini derivatives. It...