Brain Teaser: Can you find the heaviest and the lightest in 4 weighings?

This is an adaptation of a textbook programming algorithm.

Given four coins of different weights and a balance scale without standard weights, can you find the lightest and heaviest coins in four weighings?

If you had standard weights, you could use them to weigh each coin. Without standard weights, doing it in five weighings is easy. You can find the heaviest coin in 3 weighings and then the lightest coin in 2 more, but it can also be done in 4 weighings.

Bonus Question: Can you generalize to find the heaviest and lightest of 10 coins in 13 weighings?

Super Bonus Question: Can you give the formua for n coins and show that it gives the smallest number of weighings that guarantee finding the heaviest and lightest coins? (Hint: think of a convenient way of labeling the coins to show what is known about them.)