Put derivatives to work in the real world. Interpret a derivative’s meaning and units, analyze straight-line motion, solve related-rates problems, approximate values with linearization, and evaluate indeterminate limits using L’Hospital’s Rule.
Six ways to master Unit 4 — pick whichever fits how you like to study.
All 7 topics from the College Board CED, in order.
Unit 4 applies the derivatives you learned to build in context. First you interpret what a derivative means and what units it carries in an applied setting. The headline application is straight-line motion: position s(t), velocity v(t) = s′(t), and acceleration a(t) = v′(t) = s″(t) — with speed increasing when velocity and acceleration share a sign.
Related rates problems relate the rates of change of connected quantities: you differentiate a governing equation with respect to time and solve for the unknown rate. Linear approximation (linearization) uses the tangent line, L(x) = f(a) + f′(a)(x − a), to estimate values near a known point. Finally, L’Hospital’s Rule evaluates limits in the indeterminate forms 0/0 or ∞/∞ by differentiating numerator and denominator.
On the exam this unit is 10–15% for AB and 6–9% for BC, and takes about 10 class periods (AB). The four mathematical practices below run through every topic: