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Analyzing Functions flashcards
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- What does “Derivative Signs and Monotonicity” mean?Increasing and Decreasing
- Using derivative signs to describe rising and falling intervals.
- What important condition applies to derivative signs and monotonicity?Increasing and Decreasing
- A zero derivative alone does not prove a turning point.
- What does “Negative Derivative Values” mean?Increasing and Decreasing
- Interpreting a negative local rate of change.
- What important condition applies to negative derivative values?Increasing and Decreasing
- A negative slope and a negative function value are different statements.
- What does “Local and Absolute Minima” mean?Extrema
- A smallest nearby or domain-wide function value, with the scope specified.
- What important condition applies to local and absolute minima?Extrema
- A local minimum is not automatically the absolute minimum.
- What does “Closed-Interval Extrema” mean?Extrema
- Finding largest and smallest outputs on a closed interval.
- What important condition applies to closed-interval extrema?Extrema
- Never omit endpoints in a closed-interval extrema problem.
- What does “Second-Derivative Signs” mean?Concavity and Curve Sketching
- The direction in which a curve bends as its slopes change.
- What important condition applies to second-derivative signs?Concavity and Curve Sketching
- Concavity and monotonicity describe different features.
- What does “Inflection Points” mean?Concavity and Curve Sketching
- A graph point at which concavity changes direction.
- What important condition applies to inflection points?Concavity and Curve Sketching
- f″=0 alone does not establish an inflection point.