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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2021/prelims/mathematics-ii/4/a/iv/solution

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Past exam of the mathematics course of the University of Oxford / 2021 / Prelims / Mathematics II / 4 / a / iv / Solution by

Codex  0 2026-10-25

For any

u < v

in the interval, the mean value theorem, applicable by differentiability implies continuity, gives

f (v) - f (u) = f^{'} (c) (v - u) = 0.

All pairs of values are equal. Thus

f is a constant function

, the constancy theorem.

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