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 why a critical point is only a candidate for an absolute extremum. (Guide: “Step 2”; Practice Q3)
- I can explain why “only one critical point” plus a sign change gives an absolute, not just a relative, extremum. (Guide: “Why the ‘only critical point’ condition matters”; Practice Q3)
- I can tell the location of an extremum apart from its value, and give the one the question asks for. (Guide: “Step 3”; Practice Q1, Q2)
- I can explain what the maximum of a rate means, and why it is not the maximum of an amount. (Guide: “What a maximum or minimum means in context”; Practice Q5(d))
Skills
- I can use the Candidates Test on a closed domain in an applied problem, including endpoint answers. (Guide: Worked example 1; Practice Q4, Q5)
- I can justify an absolute minimum or maximum on an open domain with the first or second derivative. (Guide: Worked example 2; Practice Q6)
- I can reject critical points that lie outside the domain. (Guide: Worked example 2, step 2; Practice Q4)
- I can use a graphing calculator to find a critical point, write the setup and give answers to three decimal places. (Guide: “Using a graphing calculator”; Practice Q7)
Reasoning
- I can write a context sentence that names the quantity, gives the value with units and says when or where it happens. (Guide: Worked example 1, step 6; Practice Q5(b), Q6(c))
- I can calculate a further quantity from the optimum, such as a price, a second dimension or a time saved. (Guide: Worked example 1(b); Practice Q7(d))
- I can name the function in my justification instead of writing “it”. (Guide: “Common misconceptions”)
All ticked? Move on to Topic 5.12, Exploring Behaviors of Implicit Relations, or return to the Calculus AB roadmap or the Calculus BC roadmap.