We did the first two problems during our class time. Just copy/paste as appropriate.
Implement the bisection method. Use the stopping criterion:
(abs(b_n - a_n) / min(abs(a_n), abs(b_n))) <= tol. Show that this criterion guarantees the relative error is <= tol. Show that this method requires (something close to) 30 iterations for tol = 1e-10 for \(f(x)=x^3+4x^2-10\) on the interval \([1,2]\).Implement Newton-Raphson. Show that this method requires 4 iterations for tol = 1e-10 for \(f(x)=x^3+4x^2-10\) on the interval \([1,2]\).
Exercise 10.6.6. Don’t forget about the part of this problem on page 198!