Adventure 13 – Critical Points & DiVA Reasoning

Maximum • Minimum • Inflection Point • Using derivatives to “read” a function

🎥 Watch First (optional)

If you already know what a derivative means, you can jump straight to the activities.

Reminder: A maximum/minimum happens when the first derivative changes sign. An inflection point happens when the second derivative changes sign.

📜 Read the Story (or Listen)

ATP: The Curve Behind Every Movement — a story about how a biological curve can be studied using the same ideas as motion graphs.

Open the story page

🧩 What you will do

Activity 1: Study four “training” functions: x², −x², x³, −x³. Compute f, f′, f″ values and identify max/min/inflection.
Activity 2: Compute derivatives and find critical points. Then use a DiVA chart to draw A(t) and V(t) and draw the curve for D(t) based on the these and where the derivatives change signs (without finding many point for drawing full curves for D(t)).