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Applications of the derivative · GRE Mathematics Subject Test · Courselo

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Calculus I: limits, derivatives and their applications

Applications of the derivative

Calculus I: limits, derivatives and their applications · Lesson 4 of 4

Lesson 4 of 4

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Unit 1

Calculus I: limits, derivatives and their applications

4 lessons · 4 h 40 min of study

Functions, trigonometry and coordinate geometry1 h of study
Limits, continuity and L’Hôpital’s rule1 h 10 min of study
Differentiation techniques1 h of study
Applications of the derivativeReading · 0%

This unit is ≈15% of the GRE Math, across 4 lessons. Full syllabus

Lesson 4 of 4 · Calculus I: limits, derivatives and their applications

Applications of the derivative

3 quick checks≈5% of the testCore: Core: tested on most papers

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By the end you’ll be able to

Find tangent and normal lines, linear approximations and differentials
Locate and classify local and absolute extrema with the first- and second-derivative tests; find intervals of increase, decrease and concavity, and points of inflection
Solve optimization and related-rates problems in geometric and physical settings

Practice this skill

Adaptive questions on applications of the derivative.

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Apply Rolle’s theorem and the mean value theorem to bound functions, prove inequalities and count the real roots of equations

Deduce properties of f from the graph of f′ or f″ and sketch graphs using asymptotes, symmetry and end behaviour

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