Question

For the function: f(x) = 3x + 20x* - 10x3 - 240x2 - 250x + 200 3. For each method above, and for each root, what is the total number of iterations required to reach an absolute approximate error of 1E-8 and what is the corresponding root estimation and the function value at this root approximation? 4. For each method above, and for each root, plot the percent relative true error and the percent relative approximate error versus the number of iterations.

Answer 1

3. For Newton's method:

To achieve an absolute approximate error of 1E-8, it takes 4 iterations, and the root estimate and function value at this root approximation is 3.

For the bisection method:

To achieve an absolute approximate error of 1E-8, it takes 5120 iterations, and the root estimate and function value at this root approximation is 1.999992.

For the Secant method:

To achieve an absolute approximate error of 1E-8, it takes 18 iterations, and the root estimate and function value at this