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.
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- What does the first derivative test determine?
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Whether a critical point is a local maximum, local minimum, or neither- What is a critical point?
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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?
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The function has a local maximum there- What does it mean if f'(x) changes from negative to positive at a critical point?
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The function has a local minimum there- What does the second derivative test use to classify a critical point?
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The sign of the second derivative at that point- What does a positive second derivative at a critical point indicate?
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The function has a local minimum there (concave up)- What does a negative second derivative at a critical point indicate?
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The function has a local maximum there (concave down)- What is concavity?
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The direction in which a function's graph curves, upward or downward- What is an inflection point?
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A point where a function's concavity changes- How is an inflection point identified using the second derivative?
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It occurs where the second derivative is zero or undefined and changes sign- What is the Mean Value Theorem?
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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?
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A continuous function on a closed interval attains both a maximum and minimum value- What is an absolute (global) maximum?
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The largest value a function attains over its entire domain or a given interval- What is a local (relative) maximum?
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A point where a function's value is greater than at nearby points- What is optimization, in calculus applications?
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Using derivatives to find the maximum or minimum value of a quantity in a real-world scenario
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