Unit 4: Contextual Applications of Differentiation
Interactive practice for every topic in Unit 4. Each tool has an Explore mode and a Practice mode with fresh questions every time.
Particle Motion Lab
A particle on a number line with position, velocity and acceleration graphs. Direction, speeding up or slowing down, distance, average rates, with justification frames.
Open → Topics 4.1 and 4.3Rates in Context
What f′(a) means, with units, outside of motion: tanks, temperature, cost, river depth. Estimates from tables, rate in minus rate out, the derivative of a rate.
Open → Topics 4.4–4.5Related Rates Studio
Ladders, cones, balloons, shadows, cylinders, particles on curves and model functions. Scenes that move, the chain rule step by step, and “show that” problems.
Open → Topic 4.6Tangent Line Zoom
Zoom in until a curve looks like its tangent line. Approximations, overestimate or underestimate, and rate equations.
Open → Topic 4.7L'Hospital Lens
See why the ratio of derivatives settles 0/0. Limits from tables and formulas, ∞/∞, and working backward from a limit.
Open → Summary sheetTheorems and formulas
The definitions, theorems and formulas of Unit 4 in one place, neatly typeset. Keep it open beside a tool, or print it.
Open → Test modeTest yourself
Set up your own test on any topics here: fresh questions, a timer if you want one, and no hints or answers until you submit.
Start →Your progress is saved in this browser. To take it to another computer or browser, or to bring your points from the downloaded app, use Save a backup there and Load a backup here, under My progress.
Scores and settings stay in this browser only. No logins and no student data leave the computer. Questions marked with a gold “Calculator active” banner expect a graphing calculator; all others are non-calculator.