3.2 Special Forms

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3.2.1 Completing the Square

3.2.2 Newton-Raphson to Find Roots

When given an equation where an algebraic solution is not feasible, a numerical solution may be required. One simple technique uses an instantaneous slope of the function, and takes iterative steps towards a solution.

The function f(x) is supplied by the user along with an initial guess.

This method can become divergent if the function has an inflection point near the root.

The technique is also sensitive to the initial guess.

This calculation should be repeated until the final solution is found.

Scilab example,