 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-1/11e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The mean value theorem says that for continuous

f

[a, b]

f (b) - f (a) = f^{'} (c) (b - a)

for some

c

. Applied to

lo g

[b, a]

lo g (a / b) = \frac{a - b}{c}, b < c < a,

which gives

(a - b) / a < lo g (a / b) < (a - b) / b

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