 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-2/7h/b/solution

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

Take

(t, x), (s, y)

and

0 \leq α \leq 1

, and put

T = α t + (1 - α) s

. Then

\frac{αx + ( 1 - α ) y}{T} = \frac{α t}{T} \frac{x}{t} + \frac{( 1 - α ) s}{T} \frac{y}{s} .

Convexity of

f

, followed by multiplication by

T

, proves convexity of its perspective

g (t, x) = t f (x / t)

 New to topics? Read the docs here!