Common Core · AP Calculus AB
CHA-2.B
AP Calculus AB, Unit 2 — Represent the derivative of a function as the limit of a difference quotient.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
The 2 skills that cover it
- Derivatives & the Power RuleDefine the derivative as an instantaneous rate of change and compute it for polynomials with the power rule.Read the lesson →
- The Definition of the DerivativeBuild the derivative from scratch: an average rate over an interval, the difference quotient, and the limit that turns a secant into a tangent — then estimate it from a table or a graph, and see where a graph has no derivative at all.Read the lesson →
What a student should be able to do
- Interpret the derivative as a slope of a tangent line.
- Differentiate a power of x with the power rule.
- Differentiate a polynomial term by term.
- Evaluate a derivative at a point to get a slope.
- Find an average rate of change and simplify a difference quotient.
- Find a derivative from the limit definition.
- Estimate a derivative from a table of values or a graph, and recognise a limit as a derivative.
- Tell where a function is not differentiable, and why differentiability implies continuity.