How Much, and How Fast

You'll learnwhat a derivative means in a real situation: where its units come from, how to say it in one sentence, and why a rate is never an amount.

A dose of medicine is leaving the body. One curve answers two different questions: how much is left, and how fast it is leaving. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · UNITS FROM THE QUOTIENT · WHEN + WHAT + DIRECTION + SIZE · A RATE IS NOT AN AMOUNT · v2

M(t) = 200(0.94)^t mg left after t hours · M′(t) is how fast it changes

Before you start

What you're looking at

A dose of medicine leaving the body. The dot is how much is left, in milligrams; the pink arrow is how fast that amount is changing.

The question

What does a number like M′(3) = −10.28 actually mean?

Step 1 / 12