9.6 Tabulation function

Tabulating a function is calculating the values ​​of a function as the argument changes from some initial value to some final value with a certain step. This is how tables of function values ​​are compiled, hence the name tabulation. The need for tabulation occurs when solving a fairly wide range of tasks. For example, in the numerical solution of nonlinear equations f (x) = 0, by tabulation it is possible to separate (localize) the roots of the equation, that is, to find such segments, at the ends of which, the function has different signs. Using tabulation, you can (albeit very roughly) find the minimum of the maximum function. Sometimes it happens that a function has no analytical representation, and its values ​​are obtained as a result of calculations, which often happens when computer modeling of various processes. If such a function will be used in subsequent calculations (for example, it must be integrated or differentiated, etc.), it is often done as follows: the function values ​​are calculated in the desired interval of the argument, that is, they compile a table (tabulated), and then the table is built in some way another function defined by the analytical expression (formula). The need for tabulation also arises when constructing graphs of a function on a computer screen.