Nice Inequalities Challenge: Young’s, AM-GM & Cyclic Sums (1 Viewer)

[vuhung]

Came across this problem that ties together the Inequalities and Proofs topics really well. It’s a solid practice question for anyone looking to polish their calculus/proofs before trials.

It guides you through the whole derivation chain:

1. Part (i) & (ii): Using calculus (minimisation) to derive Young's Inequality.
2. Part (iii): The classic induction proof for AM-GM.
3. Part (iv): A satisfying application involving a cyclic sum.

Good luck! Let me know if you get stuck on the algebra in part (i).