Common Core · AP Calculus AB
FUN-3.F
AP Calculus AB, Unit 3 — Determine higher-order derivatives of a function.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
AP Calculus AB, Unit 3 — Determine higher order derivatives of a function.
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
- Concavity & Curve SketchingUse the second derivative to read the bend of a graph: concave up or down, inflection points, the second derivative test, and the shape that the signs of f′ and f″ together force — then assemble the features of a curve before drawing it.Read the lesson →
- Higher-Order DerivativesDifferentiate again and again: second, third and nth derivatives of polynomials, exponentials, sines and reciprocals, the patterns they fall into, and what each order means.Read the lesson →
What a student should be able to do
- Find the second derivative and the intervals of concavity.
- Find inflection points and classify stationary points with the second derivative test.
- Match the shape of a graph to the signs of the first and second derivatives.
- Collect the features of a curve — intercepts, asymptotes, extrema, concavity — for a sketch.
- Find the second, third and fourth derivatives of a polynomial and evaluate them at a point.
- Follow the cycle of sin and cos and the powers of ekx to a named higher derivative.
- Find the second derivative of a product or a composition, and read f'' as acceleration and f''' as jerk.
- Read the pattern of the nth derivative of 1/x and xn, and relate fk(0) to a coefficient.