Rootfinding...(Numerical analysis)?

Question

Let β be a unique root of:

x = 3 / (1 + x^4)

Find an interval [a,b] containing β and for which the bisection method will converge to β. Then estimate the number of iterates needed to find β within an accuracy of 5x10^-5

10 pts for best, thanks to all who answer

Answer 1

The he root is 1.13, and the interval is 1  Ã¢Â‰Â¤ x ≤ 2

f(x) = x - f(x)/f'(x)

f(x) = x - 3/(1 + x^4)

We need 15 iterates,  2^-15 = (do it in your calculator and you'll see)