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Applications of Derivatives: Curve Sketching and Optimization

10th Grade · Math · Open Global Math

10 lessons

Goal

Apply first and second derivatives to analyze monotonicity, concavity, points of inflection, graph behavior, and solve real-world optimization problems.

10 lessons
0 of 10 done
  1. Equations of Tangent Lines and Normal Lines to CurvesUp next
  2. Locating Stationary Points on Polynomial and Rational CurvesNot started yet
  3. Increasing and Decreasing Intervals and the First Derivative TestNot started yet
  4. Second Derivatives, Concavity, and Points of InflectionNot started yet
  5. Maxima and Minima: First and Second Derivative TestsYou are here
  6. Comprehensive Curve Sketching for Polynomial and Rational FunctionsNot started yet
  7. Curve Sketching with Exponential, Logarithmic, and Trigonometric FunctionsNot started yet
  8. Formulating Optimization Problems from Geometric and Physical ModelsNot started yet
  9. Solving Single-Variable Optimization ProblemsNot started yet
  10. Applied Optimization in Economics, Science, and EngineeringNot started yet
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Learning standards covered

GlobalOGM.11.CAL.2Open Global Math Standards 2026™ · 10th Grade

Interpret derivatives as average and instantaneous rates of change and tangent slopes; compute first and second derivatives of polynomial, rational, exponential, logarithmic, and trigonometric functions; and apply derivatives to curve sketching (concavity, inflection points) and optimization problems.