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Second-derivative analysis and curve sketching · AP Calculus AB · Courselo

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Calc AB
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Unit 5: Analytical applications of differentiation

Second-derivative analysis and curve sketching

Unit 5: Analytical applications of differentiation · Lesson 4 of 5

Lesson 4 of 5

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Unit 5

Unit 5: Analytical applications of differentiation

5 lessons · 8 h 30 min of study

Extrema and critical points1 h 30 min of study
Mean Value Theorem and related results1 h 15 min of study
First-derivative analysis1 h 45 min of study
Second-derivative analysis and curve sketchingReading · 0%
Optimization with derivatives2 h of study

This unit is ≈17% of the Calc AB, across 5 lessons. Full syllabus

Lesson 4 of 5 · Unit 5: Analytical applications of differentiation

Second-derivative analysis and curve sketching

3 quick checks≈4% of the testStretch: Stretch: harder material that separates the top grades

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By the end you’ll be able to

Determine intervals of concavity from $f''(x)$ or from the behavior of $f'(x)$.
Identify possible points of inflection and justify whether they occur.
Apply the second derivative test when valid.
Infer properties of $f$ from graphs of $f'$ or $f''$.

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Adaptive questions on second-derivative analysis and curve sketching.

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Sketch a function consistent with derivative, concavity, and asymptotic information.

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