Prove or provide a counter example: if f has a double root at x = p then there is some open interval (a, b), a < p < b, for which the fixed point algorithm will work with h.

Given

x f(x)

0 0.00000000

1 0.3836

2 -2.0646

3 8.2776

4 -29.2959

And for physical reasons, you know that |f⁽⁵⁾ | < 15000 and |f⁽⁴⁾| < 5500. Provide an approximate graph for f, approximate any roots, and find f ' at the given points. Also approximate and give some bound for your approximation.