🚀 Adventure 2 — The Apple and the Secret of Slope
Story, video, and a short activity that zooms in on a second‑degree curve to reveal a tangent line.
🎯 What you will learn
How to omplete a table to study acurve, and use the tangent line to understand slope at one instant.
How to find the slope of a tangent using rise/run.
📖 1) Read / Listen: Story
First, read The Apple and the Secret of Slope.
This is the Newton–Leibniz story that sets the stage: a curve can have a slope at a single instant.
🎥 2) Watch the Video
Watch the 3Blue1Brown video Open:paradox of the derivative | Chapter 2, Essence of calculus where a secant line slides and becomes a
tangent line. That “zooming in” is the whole secret.
✏️ 3) Do the Adventure Activity
📈 4) What You Will Discover
One idea powers this Adventure:
- Slope = instantaneous change
- What does it mean for a curve to have a slope “right now”?
- Why does zooming in make the curve look like a straight line?
- How does the slope change as t gets larger?
- How does rise/run on the tangent match the limit idea?
💡 6) If You Get Stuck
Pick two points close together, compute rise/run, then make them even closer.
The slope you’re chasing is exactly what the tangent line captures.