AP Calculus AB, unit: Analytical Applications of Differentiation. Conceptual understanding and key rules for this unit, explained in plain language alongside the formula. Front: a concept or short problem cue. Back: the explanation, rule, or answer.
16 cards · basic cards · AI-written, checked twice. Edit anything.
- What does the first derivative test determine?
- Whether a critical point is a local maximum, local minimum, or neither
- What is a critical point?
- A point where a function's derivative is zero or undefined
- What does it mean if f'(x) changes from positive to negative at a critical point?
- The function has a local maximum there
- What does it mean if f'(x) changes from negative to positive at a critical point?
- The function has a local minimum there
- What does the second derivative test use to classify a critical point?
- The sign of the second derivative at that point
- What does a positive second derivative at a critical point indicate?
- The function has a local minimum there (concave up)
- What does a negative second derivative at a critical point indicate?
- The function has a local maximum there (concave down)
- What is concavity?
- The direction in which a function's graph curves, upward or downward
- What is an inflection point?
- A point where a function's concavity changes
- How is an inflection point identified using the second derivative?
- It occurs where the second derivative is zero or undefined and changes sign
- What is the Mean Value Theorem?
- If a function is continuous and differentiable on an interval, some point has a derivative equal to the average rate of change
- What is the Extreme Value Theorem?
- A continuous function on a closed interval attains both a maximum and minimum value
- What is an absolute (global) maximum?
- The largest value a function attains over its entire domain or a given interval
- What is a local (relative) maximum?
- A point where a function's value is greater than at nearby points
- What is optimization, in calculus applications?
- Using derivatives to find the maximum or minimum value of a quantity in a real-world scenario
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