Related Rates

What The Heck Are Related Rates? (free)

If you haven't watched a lot of my other videos, this one might come as a bit of a surprise. But as someone who's tutored a LOT of related rates, I know the one thing that almost every student is confused by, so I'm going to take almost the full length of this first video to drill it into your brain. You're welcome! :)

Basic Related Rates Problems

When it comes to related rates, there aren't really any "basic" ones; this is the hardest topic in derivatives. But these problems are at least pretty straightforward: if you need to use the area formula for a circle, the words "area" and "circle" are going to be in the problem. That might not sound like much, but it's a lot more of a hint than they'll give you in the hard ones of the later videos.

Triangle-Based Word Problems

Approximately half of related word problems seem to involve triangles in one form or another, either requiring the Pythagorean Theorem, special triangles, or SohCahToa. Sorry this video is so long, but we've got a lot of nuance to cover: planes and radar; roller derby teams colliding; ladders sliding down UPS trucks; and a similar triangles problem where a dude is chasing his own shadow!

Area Related Rates Problems (AP level)

This video is pretty long too, but it only covers three problems because they're pretty tough. We'll explore an oil slick spreading across a floor, an ice cream cone filling with hot fudge, and a wacky 30-60-90 sundial.

Volume Related Rates Problems (AP level)

More hard problems, this time with the theme of volume: helium balloon leaking helium (hint: negative rate); yet another ice cream cone example; and a cool modern art museum example with concrete molds.