Chapter 2.5, Problem 10ES

Use Steffensen’s method with p₀ = 3 to compute an approximation to $\sqrt[3]{25}$ accurate to within 10⁻⁴. Compare this result with the results obtained in Exercise 12 of Section 2.2 and Exercise 13 of Section 2.1.

12. Use a fixed-point iteration method to find an approximation to $\sqrt[3]{25}$ that is accurate to within 10⁻⁴. Compare your result and the number of iterations required with the answer obtained in Exercise 13 of Section 2.1.

13. Find an approximation $\sqrt[3]{25}$ correct to within 10⁻⁴ using the Bisection Algorithm. [Hint: Consider f(x) = x³ − 25.]