BC-only material. Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. Prerequisites (Topics 9.1, 9.2, 2.8, 3.1) are on the Calculus BC roadmap.
Understanding
- I can explain what a vector-valued function is and how its position vector traces a curve. (Guide: “What is a vector-valued function?”)
- I can explain, from the limit definition, why r′(t) is found one component at a time. (Guide: “The derivative: one component at a time”)
- I can explain why r′(t) is tangent to the curve and points in the direction of increasing t. (Guide: “What r′(t) tells you about the curve”; Figure 1)
Skills
- I can find the domain of a vector-valued function from both of its components. (Guide: “Domain”; Practice Q2)
- I can find r′(t) and r″(t), using the product and chain rules inside components. (Guide: Worked example 1; Practice Q1, Q5(a), Q6(a))
- I can find the slope of the tangent line and write its equation at a given t. (Guide: Worked example 1; Practice Q6(c))
- I can find where a curve has horizontal or vertical tangents, checking that the other component is not zero. (Guide: Worked example 2; Practice Q5(b))
- I can estimate r′(t) from a table using difference quotients, with units. (Practice Q7(a))
Reasoning
- I can describe the direction of motion from the signs of the components of r′(t). (Guide: Worked example 2; Practice Q3, Q6(d), Q7(d))
- I can explain the difference between the vector r″(t) and the scalar d²y/dx², and compute both. (Guide: “r″(t) is not d²y/dx²”; Practice Q4)
- I can interpret a component of r′(t) or r″(t) in context, with units. (Guide: Worked example 2; Practice Q7(b), Q7(c))
All ticked? Move on to the Topic 9.5 study guide, Integrating Vector-Valued Functions, or return to the Calculus BC roadmap.