Work through the list without notes. 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 that a derivative is a rate of change in any context, not only in motion, and give three examples with units. (Guide: “One idea, many settings”)
- I can explain the difference between an amount f(a), an average rate over an interval and an instantaneous rate f′(a). (Guide: Worked example 1(c); Practice Q2, Q5(c))
- I can explain why f′(a) gives only an approximate change over the next unit of input. (Guide: “Writing an interpretation”; Practice Q7(d))
- I can interpret a rate when the input is not time, such as altitude, distance or number of items. (Guide: “When the input is not time”; Practice Q1, Q5)
Calculation
- I can find the units of f′ and f″ from the units of f and of its input. (Guide: “Units”; Practice Q2, Q6)
- I can find a rate of change from a formula, using any differentiation rule I need. (Guide: Worked example 1; Practice Q2, Q6, Q7)
- I can estimate a rate of change from a table using the nearest values either side, and say “approximately”. (Guide: Worked example 2; Practice Q3)
Reasoning
- I can write a four-part interpretation: when, what, increasing or decreasing, and rate with units. (Guide: “Writing an interpretation”; Practice Q1, Q5(b), Q7(b))
- I can avoid double negatives by putting the sign either in the word or in the number, not both. (Guide: “Writing an interpretation”; Practice Q6(c))
- I can use the signs of f′ and f″ together to say whether a quantity is changing faster or more slowly. (Guide: “What the second derivative adds”; Practice Q4, Q6(d))
All ticked? Move on to Topic 4.4, Introduction to Related Rates, or return to the Calculus AB roadmap or the Calculus BC roadmap.