Potions heal for a small amount instantly and you move faster while being healed by them.
+9% Attack Speed
+6 Armor or 8 MR (match-up)
Conqueror's ramping damage in extended duels is perfect for Jax's auto-attack based fight pattern, allowing you to pump out massive damage over time.
Jax is a solid tower diver and Triumph's big heal can make the difference between life and deal in sticky situations.
All of Jax's damage comes from his ability to auto attack repeatedly and Alacrity helps your early game trades and skirmishes massively before you're able to build any significant Attack Speed. It also allows you to opt into more defensive items so you can prolong the trade.
WhyCoup De Grace
Your rune choice here largely depends on if your laning against a tank or not. Coup De Grace is good at killing squishy champions.
If you are laning against a tank, take Cut Down.
Magical Footwear's raw mid-game gold value accelerates you into a quicker 2nd item power-spike.
WhyTime Warp Tonic
Time Warp Tonic pairs well with with your Corrupting Potion start for strong dueling.