lesson
Comprehensive Curve Sketching for Polynomial and Rational Functions
Synthesize intercepts, asymptotes, symmetry, stationary points, concavity, and inflection points to sketch polynomial and rational curves.
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Applications of Derivatives: Curve Sketching and Optimization
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
- Equations of Tangent Lines and Normal Lines to CurvesUp next
- Locating Stationary Points on Polynomial and Rational CurvesNot started yet
- Increasing and Decreasing Intervals and the First Derivative TestNot started yet
- Second Derivatives, Concavity, and Points of InflectionNot started yet
- Maxima and Minima: First and Second Derivative TestsNot started yet
- Comprehensive Curve Sketching for Polynomial and Rational FunctionsYou are here
- Curve Sketching with Exponential, Logarithmic, and Trigonometric FunctionsNot started yet
- Formulating Optimization Problems from Geometric and Physical ModelsNot started yet
- Solving Single-Variable Optimization ProblemsNot started yet
- Applied Optimization in Economics, Science, and EngineeringNot started yet
Learning standards covered
OGM.11.CAL.1Open Global Math Standards 2026™ · 10th GradeUnderstand continuous functions, calculate limits (including indeterminate forms 0/0 and ∞/∞ via algebraic methods and L'Hopital's rule), identify vertical/non-vertical asymptotes, and apply infinite numerical approximation techniques.
OGM.11.CAL.2Open Global Math Standards 2026™ · 10th GradeInterpret 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.