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Extrema and critical points · AP Calculus AB · Courselo

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Calc AB
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Unit 5: Analytical applications of differentiation

Extrema and critical points

Unit 5: Analytical applications of differentiation · Lesson 1 of 5

Lesson 1 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 pointsReading · 0%
Mean Value Theorem and related results1 h 15 min of study
First-derivative analysis1 h 45 min of study
Second-derivative analysis and curve sketching2 h of study
Optimization with derivatives2 h of study

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

Lesson 1 of 5 · Unit 5: Analytical applications of differentiation

Extrema and critical points

3 quick checks≈3% of the testCore: Core: tested on most papers

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By the end you’ll be able to

Find critical points by solving $f'(x)=0$ or identifying where $f'(x)$ does not exist.
Determine absolute extrema on a closed interval.
Distinguish between relative and absolute extrema.
Use endpoint values and critical-point values to justify a closed-interval answer.

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Adaptive questions on extrema and critical points.

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0% read

Apply the Extreme Value Theorem to justify that a continuous function on a closed interval must attain an absolute maximum and an absolute minimum.

Explain when the hypotheses of the Extreme Value Theorem are not satisfied, so existence of absolute extrema is not guaranteed.

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PreviousLocal linearity and linearization Next lessonMean Value Theorem and related results