 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability-resit/6/d/solution

f

x_{n}

y = f (x_{n}) + f^{'} (x_{n}) (x - x_{n})

. Its intersection with the horizontal axis gives Newton's method:

x_{n + 1} = x_{n} - \frac{f ( x _{n} )}{f ^{'} ( x _{n} )} .

Each step requires

f^{'} (x_{n}) \neq = 0

. Convergence to a zero of a function additionally depends on the starting point and the local behavior of

f

; the update formula alone is not a convergence guarantee.

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