 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/discrete-mathematics-probability-and-continuous-mathematics/6/d/solution

h = x_{n + 1} - x_{n} = - f (x_{n}) / f^{'} (x_{n})

f (x_{n + 1}) = f (x_{n}) + h f^{'} (x_{n}) + \frac{h ^{2}}{2} f^{''} (ξ) .

f (x_{n + 1}) = \frac{( x _{n + 1} - x _{n} ) ^{2}}{2} f^{''} (ξ),

with

ξ

between the consecutive iterates. In particular, a nonzero step has negative new residual under the stated strict concavity.

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