Common Core · AP Calculus AB
FUN-4.B
AP Calculus AB, Unit 5 — Calculate minimum and maximum values in applied contexts or analysis of functions.
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 — Solve optimization problems and justify the answer.
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
- Applications of DerivativesUse derivatives to find tangent lines, velocities, and maximum and minimum values.Read the lesson →
- OptimizationTurn a word problem into a function of one variable and find its best value: two numbers, a fenced field, an open box, a can of least material, the closest point, the best price.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.
- Write the constraint and the quantity to optimise, then reduce to one variable.
- Find the critical number and justify that it gives a maximum or a minimum.
- Solve box, fence, distance and revenue problems exactly.
- Check both endpoints of a closed domain against the critical numbers, and reject a critical number that lies outside it.