Work through the list without notes or a calculator. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can explain what “related rates” means: quantities linked by an equation have linked rates of change. (Guide: “Quantities that change together”)
- I can explain why differentiating s³ with respect to t gives 3s² · ds/dt, and why the factor ds/dt is there. (Guide: “The chain rule does the linking”; Practice Q1)
- I can sort the information in a problem into facts true at all times and values true only at one instant. (Guide: “Always true, or only true now?”; Practice Q5(a))
- I can explain why substituting instant values before differentiating gives a wrong answer. (Guide: “Always true, or only true now?”; Practice Q5(c))
Skills
- I can differentiate an equation term by term with respect to t, attaching a rate to every changing quantity. (Guide: reference table; Practice Q6(a))
- I can use the product rule when two changing quantities are multiplied. (Guide: Worked example 2(a); Practice Q2, Q3, Q7)
- I can use the quotient rule when one changing quantity is divided by another. (Guide: Worked example 2(b); Practice Q4)
- I can give a decreasing quantity a negative rate and report the answer with units. (Guide: Worked example 1; Practice Q5(b))
Reasoning
- I can use units and signs to check whether a related rate answer is sensible. (Guide: Worked example 1 “Check”)
- I can explain why the same equation gives different rates at different instants. (Practice Q6(d))
- I can explain which terms of a product-rule derivative make a quantity grow or shrink overall. (Guide: Worked example 2(a); Practice Q7(c))
All ticked? Move on to Topic 4.5, Solving Related Rates Problems, or return to the Calculus AB roadmap or the Calculus BC roadmap.