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2.2.2 Line Search and Trust Region Steps     continued...

For example, at the first step, a cubic polynomial can be constructed from the two function values , and the two slopes , . The slopes are the directional derivatives defined as: . Note in Fig. 6 a negative slope at since is a descent direction. More generally, for the bracketed interval , and corresponding function and slopes , the cubic polynomial passing through and and having the specified slopes is given by:

where