Care must be taken that  not be too small, which would cause an overflow error by the computer. This may occur if  due to the finite precision of the machine. This may also give a misleading result for the convergence test of . To avoid that, we might use the relative deviation to test for convergence.
c. Compare and contrast
Both the Newton-Raphson and Secant Methods locate just one root at a time.
Newton: requires evaluation of f and of  at each step; converges rapidly.
Secant: requires evaluation only of f at each step; converges less rapidly.
A hybrid method combines the use in one program of two or more specific methods. For instance, we might use bisection to locate a root roughly, then use the Secant Method to compute the root more precisely. For instance, we might use bisection to locate multiple roots of an equation, then use Newton-Raphson to refine each one.
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