Evolution of cetaceans "Caperea marginata") all have derived characteristics presently unknown in any cetothere and vice versa (such as a sagittal crest). The adaptation of echolocation occurred when toothed whales (Odontoceti) split apart from baleen whales, and distinguishes modern toothed whales from fully aquatic archaeocetes. This happened around 34 million years ago in a second cetacean radiation. Modern toothed whales do not rely on their sense of sight, but rather on their sonar to hunt prey. Echolocation also allowed toothed whales to dive deeper in search of food, with light no longer necessary for navigation, which opened up new food sources. Toothed whales
Divided differences "ƒ" on the nodes "x", ..., "x" are used: etc. Divided differences for formula_12 and the first few values of formula_13: To make the recursive process more clear, the divided differences can be put in a tabular form: The divided difference scheme can be put into an upper triangular matrix. Let formula_24. Then it holds formula_44 With the help of a polynomial function formula_45 with formula_46 this can be written as Alternatively, we can allow counting backwards from the start of the sequence by defining formula_48 whenever formula_49 or formula_50. This definition allows formula_51 to be interpreted as formula_52, formula_53