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 the difference between a local maximum and an absolute maximum, using a graph. (Guide: “Local versus absolute” and Figure 1; Practice Q1)
- I can explain why an absolute extremum inside a closed interval must be at a critical point. (Guide: “Where can an absolute extremum be?”)
- I can state the two conditions the Candidates Test needs and say what can go wrong without them. (Guide: “When the test does not apply”; Practice Q4)
Skills
- I can find every critical point inside an interval, including points where f′ does not exist. (Guide: Worked example 2; Practice Q3, Q5(b))
- I can discard critical points that lie outside the interval. (Guide: Worked example 1; Practice Q5(b))
- I can build a table of candidates and evaluate f at each, with exact values. (Guide: Worked examples 1 and 2; Practice Q2, Q5(c))
- I can compare exact values such as −3∛4 and −6 without a calculator. (Guide: Worked example 2, step 5)
- I can use a calculator to evaluate candidates and give answers to 3 decimal places without rounding early. (Practice Q6)
Reasoning
- I can state an absolute extremum as a value of f and say where it occurs, including ties. (Guide: “How to write the answer”; Practice Q3)
- I can justify an answer by naming continuity on the closed interval and the candidates. (Practice Q5(c), Q6(b))
- I can explain why decreasing at an endpoint does not make that endpoint the minimum. (Practice Q6(c))
- I can decide whether a function has an absolute maximum on an open interval and explain why. (Practice Q7(c))
All ticked? Move on to Topic 5.6, Determining Concavity of Functions over Their Domains, or return to the Calculus AB roadmap or the Calculus BC roadmap.