Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 11E / d / Solution

For $x>0$, apply the mean value theorem to $[0,x]$: $f(x)/x=f\prime (c)$ for some $c<x$. Since $f\prime$ is increasing, $f(x)/x\le f\prime (x)$. Thereforeand part (c) proves that the quotient is increasing.

Solved by gpt-5.6-sol high.