Differentiation and Integration
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In the solution of practical problems, one often encounters derivatives and integral of a function f defined in a certain interval. In many cases, the function f is so complicated that even the powerful tools of calculus are either difficult to apply or become totally infructuous. In other cases, f may be defined in a tabular form, to which the results of calculus do not apply. In such difficulties, numerical answers may be sought by approximating the function f by an interpolating polynomial \(\phi \) obtained from a table of values of f(x), which if not given, may be constructed from the analytical definition of f.