Work through the list without notes. Use a calculator only for the statement that says so. 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 why a table or a graph lets me estimate f′(a) but never find it exactly. (Guide: “Why estimate a derivative?”)
- I can explain why a symmetric difference quotient is usually closer to f′(a) than a one-sided one. (Guide: “Three difference quotients”, Figure 1; Practice Q6(d))
- I can state the units of a derivative as units of f per unit of x. (Guide: “Estimating from a table”; Practice Q3)
Skills
- I can choose the closest table values on an interval containing a and write the difference quotient with those values. (Guide: Worked example 1; Practice Q1, Q5(a))
- I can divide by the change in x, even when a table is unevenly spaced. (Guide: Worked example 1; Practice Q1)
- I can estimate f′(a) from a drawn tangent using two points on the line. (Guide: Worked example 2; Practice Q2)
- I can work out forward, backward and symmetric estimates for a given h. (Guide: “Three difference quotients”; Practice Q4, Q7(b))
- I can find f′(a) with a calculator’s numerical derivative and write the setup and a three-decimal answer. (Guide: Worked example 3; Practice Q6(c)) Calculator allowed.
Reasoning
- I can interpret a derivative estimate in context: the moment, the quantity, the direction and the rate with units. (Guide: “Writing a complete answer”; Practice Q3, Q5(b))
- I can choose between possible table intervals and justify my choice. (Guide: “Special cases in a table”; Practice Q5(c), Q7(c))
- I can check that the sign of my estimate matches whether the graph or data are rising or falling. (Guide: “Estimating from a graph”; Practice Q7(d))
- I can explain why a calculator’s number may be misleading at a corner. (Guide: “Common misconceptions”)
All ticked? Move on to Topic 2.4: Connecting Differentiability and Continuity, or return to the Calculus AB roadmap or the Calculus BC roadmap.