Several types of functions have been considered in the previous chapters. In all cases it has been assumed that the functions are continuous functions of some independent variable or variables. It has been further assumed that a mathematical expression or a computer algorithm exists that will respond with the value of the function when given a set of values of the independent variables. For a single variable this can be expressed as:
$${\rm{Given}}:f\left( x \right)for\,x_1 < x < x_2.$$
(6.1)
Extensive use has been made of the ability to take a derivative of such a function at any desired point within the allowed range of values of the independent variable. This has been used in such functions as newton() and nsolv() for obtaining the zeros or roots of functions.

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