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 state the definition of the derivative function f′(x), including “provided the limit exists”. (Guide: “From a number to a function”; Practice Q3)
- I can explain the difference between the function f′(x) and the number f′(a). (Guide: “Common misconceptions”; Practice Q2, Q5(d))
- I can explain why f′ may exist at fewer inputs than f, with an example. (Guide: “Where f′ exists”; Practice Q5(b))
- I can explain that f′(a) is the slope of the tangent line at (a, f(a)). (Guide: “The tangent line” and Figure 1)
Skills
- I can find f′(x) from the definition for a polynomial. (Guide: Worked example 1; Practice Q6(a), Q7(a))
- I can find f′(x) from the definition for a rational function or a square-root function. (Guide: Worked example 2; Practice Q5(a))
- I can read and write f′(x), dy/dx, y′ and “dy/dx at x = a” correctly. (Guide: “Derivative notation”; Practice Q1, Q7(d))
- I can write the equation of a tangent line in point-slope form. (Guide: Worked example 3; Practice Q2, Q5(c), Q6(c))
- I can find the points where a tangent line has a given slope. (Practice Q6(b))
Reasoning
- I can state the units of a derivative and interpret its value and sign in context. (Guide: “Four representations”; Practice Q4, Q7(b))
- I can describe one derivative analytically, numerically, graphically and in words. (Guide: “Four representations of a derivative”)
- I can spot and explain the error when someone substitutes into f instead of f′. (Guide: “Two common slips”; Practice Q7(d))
All ticked? Move on to Topic 2.3, Estimating Derivatives of a Function at a Point, or return to the Calculus AB roadmap or the Calculus BC roadmap.