Common Core · AP Calculus AB
FUN-4.A
AP Calculus AB, Unit 5 — Justify conclusions about the behaviour of a function based on the behaviour of its derivatives.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
AP Calculus AB, Unit 5 — Justify conclusions about the behaviour of a function based on the behaviour of its derivatives: concavity, inflection points, the second derivative test, sketching.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
AP Calculus AB, Unit 5 — Justify conclusions about the behaviour of a function based on the behaviour of its derivatives: intervals of increase and decrease, the first derivative test, absolute extrema.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
The 3 skills that cover it
- Applications of DerivativesUse derivatives to find tangent lines, velocities, and maximum and minimum values.Read the lesson →
- 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 →
- Increasing, Decreasing & ExtremaRead the sign of the derivative as the direction of the graph: critical numbers, intervals of increase and decrease, the first derivative test for local extrema, absolute extrema on a closed interval, and the Mean Value Theorem.Read the lesson →
What a student should be able to do
- Write the equation of a tangent line at a point.
- Relate position, velocity and acceleration.
- Find critical points and classify maxima and minima.
- Solve a simple optimisation problem.
- 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 critical numbers of a function.
- Find the intervals where a function increases and decreases from the sign of its derivative.
- Classify local extrema with the first derivative test, from a rule or a graph of the derivative.
- Find absolute extrema on a closed interval, and the point the Mean Value Theorem promises.