ROOTS OF EQUATIONS

At the end of this section, students should be able to:

  1. test for the existence of a root of \(f(x)=0\) where f is continuous using the Intermediate Value Theorem;
  2. use interval bisection to find an approximation for a root in a given interval;
  3. use linear interpolation to find an approximation for a root in a given interval;
  4. explain, in geometrical terms, the working of the Newton-Raphson method;
  5. use the Newton-Raphson method to find successive approximations to the roots of \(f(x)=0\), where \(f\) is differentiable;
  6. use a given iteration to determine a root of an equation to a specified degree of accuracy.