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 what it means for f to be increasing or decreasing on an interval, by comparing f(x₁) and f(x₂). (Guide: “What increasing and decreasing mean”)
- I can explain, using the Mean Value Theorem, why f′(x) > 0 on an interval makes f increasing there. (Guide: “The link to the derivative”)
- I can explain why a single zero of f′, with the same sign on both sides, does not end an interval of increase. (Guide: the x³ example; Practice Q2)
- I can explain the difference between f′ being positive and f′ being increasing. (Guide: Worked example 2 “The trap”; Practice Q4, Q6(d))
Skills
- I can differentiate, factor f′ and build a sign chart with test values or factor signs. (Guide: Worked example 1; Practice Q1, Q3)
- I can include every split point: zeros of f′, points where f′ is undefined, and gaps in the domain of f. (Guide: “When the domain has a gap”; Practice Q7)
- I can read the intervals where f increases or decreases from a graph of f′. (Guide: Worked example 2, Figure 1; Practice Q5)
- I can find where a quantity is increasing in context from the sign of its rate, and give units. (Guide: “Increasing and decreasing in context”; Practice Q6)
Reasoning
- I can write a justification that names f (or the quantity), the interval and the sign of f′. (Guide: “Writing a justification”; Practice Q5, Q6)
- I can compare two values of f, such as f(3) and f(1), using an interval where f is increasing or decreasing. (Practice Q5(d), Q6(c))
- I can explain why I must not join intervals across a point where f is undefined. (Guide: h(x) = x + 4/x)
All ticked? Move on to Topic 5.4, Using the First Derivative Test to Determine Relative (Local) Extrema, or return to the Calculus AB roadmap or the Calculus BC roadmap.