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 use the limit definition to show that the derivative of a constant is 0. (Guide: “1. Constant rule”)
- I can explain how the constant multiple and sum rules follow from properties of limits. (Guide: “The four rules”)
- I can explain with a graph why adding a constant does not change the derivative. (Guide: Figure 1; Practice Q5(c))
- I can explain why the rules do not let me split a product or a quotient. (Guide: Worked example 2; Practice Q3, Q6(b))
Skills
- I can differentiate a polynomial term by term, keeping coefficients and dropping constant terms. (Guide: “Differentiating polynomials term by term”; Practice Q1, Q5(a))
- I can treat numbers such as π² as constants. (Practice Q1)
- I can expand brackets or split a fraction with a one-term denominator before differentiating. (Guide: “Rewrite first”; Practice Q3, Q6)
- I can combine derivative values from a table using the sum, difference and constant multiple rules. (Guide: “Unknown functions”; Practice Q2)
- I can find the equation of a tangent line to a polynomial at a given point. (Guide: Worked example 1; Practice Q7(c))
- I can find the points where a graph has a horizontal tangent. (Guide: Worked example 3; Practice Q4)
Reasoning
- I can interpret a derivative value as a rate of change, with units, in context. (Practice Q5(b))
- I can use a derivative to show that a rate is always positive. (Practice Q5(d))
- I can set up and solve equations for unknown coefficients from a point and a slope. (Practice Q7(a))
- I can explain why a given slope is impossible for a curve. (Practice Q7(d))
All ticked? Move on to Topic 2.7, Derivatives of cos x, sin x, eˣ and ln x, or return to the Calculus AB roadmap or the Calculus BC roadmap.