 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ia/paper-1/10f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Differentiability at

x_{0}

\frac{f ( x ) - f ( x _{0} )}{x - x _{0}} ⟶ f^{'} (x_{0}) .

Hence

f (x) - f (x_{0}) = (x - x_{0}) (f^{'} (x_{0}) + o (1)) \to 0

x \to x_{0}

. Therefore every differentiable function is continuous at each point where it is differentiable.

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