Mathematical formulas

Differential Calculus

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Sections

  • 1Notation, functions and domains▸
  • 2Limits▸
  • 3Continuity▸
  • 4Derivative and geometric interpretation▸
  • 5Differentiation rules▸
  • 6Higher-order derivatives▸
  • 7Mean value theorem▸
  • 8Function analysis▸
  • 9Optimization▸
    • 9.1General procedure
    • 9.2Criteria on closed intervals
  • 10Linear approximations and differentials▸
  • 11Taylor series (introduction)▸
  • 12L'Hôpital and indeterminate limits▸
  • 13Implicit and related functions▸
  • 14Related rates▸
  • 15Graphs and asymptotic behavior▸
  • 16Guide to differentiate and analyze▸
  • AAppendix A: extended derivative table▸
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Featured topics

Optimization

Find maxima and minima with derivative tests and apply the method to optimization problems.

Key formulas

  • DIF-093

    Second derivative test (maximum).

  • DIF-094

    First derivative test.

  • DIF-095
  • DIF-087

Related sections

  • 9. Optimization
  • 8. Function analysis

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