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 f′(a) as the rate at which f changes per unit of input, at the single input value a. (Guide: “What a derivative measures”; Practice Q2)
- I can say what the sign of a derivative tells me about the quantity in context. (Guide: “What a derivative measures”; Practice Q5(b))
- I can tell apart f(a), an average rate over an interval and f′(a), and give the units of each. (Guide: Worked example 1; Practice Q6(c), Q7(b))
- I can explain why f′(a) only approximates the change in f over the next unit of input. (Guide: Worked example 1; Practice Q5(c))
Skills
- I can find the units of a first or second derivative from the units of the function and of its input. (Guide: “Units of a derivative”; Practice Q1, Q4)
- I can convert a rate to different units, such as per minute to per hour or metres to centimetres. (Guide: Worked example 2; Practice Q6(b))
- I can estimate a derivative from a table using the closest data on either side. (Guide: Worked example 2; Practice Q3, Q6(a))
- I can find a derivative from a formula and state it with units. (Guide: Worked example 1; Practice Q5(a))
- I can estimate a small change in a quantity as rate × step. (Guide: Worked example 3; Practice Q7(c))
Reasoning
- I can write a four-part interpretation sentence: quantity, input value, direction, rate with units. (Guide: “Writing an interpretation sentence”; Practice Q5, Q6(b), Q7(a))
- I can interpret a second derivative in context as the rate at which a rate is changing, including when the first derivative is negative. (Guide: Worked example 3; Practice Q4, Q6(d) for the positive case)
- I can use units to check that a combined rate makes sense. (Practice Q7(d))
All ticked? Move on to Topic 4.2, Straight-Line Motion: Connecting Position, Velocity, and Acceleration, or return to the Calculus AB roadmap or the Calculus BC roadmap.