Public learning track
Applications of Derivatives: Extrema and Optimization
12th Grade · Math · Open Global Math
7 lessons
Goal
Determine tangent and normal equations, find extrema, analyze curve behavior, and solve real-world optimization problems.
Featured Diagrams
Equations of Tangents and Normals to Explicit Curves
7 lessons
0 of 7 done
- 1Equations of Tangents and Normals to Explicit CurvesUp nextStart
- 2Tangents and Normals to Implicitly Defined CurvesPremiumNot started yet
- 3Intervals of Increase, Decrease, and Local ExtremaNot started yet
- 4Curve Sketching with Exponential, Logarithmic, and Trigonometric FunctionsNot started yet
- 5Applied Optimization: Geometric Area and Volume ProblemsNot started yet
- 6Applied Optimization: Economic and Cost Minimization ModelsNot started yet
- 7Applied Optimization: Distance, Time, and Kinematic ProblemsNot started yet
Standards Covered
- OGM.13.CAL.4Open Global Math Standards 2026™ · Math · Level 13 / High School 4 (Age 17–18) · Grade 12Apply differentiation to determine equations of tangents and normals, identify stationary points, local extrema, intervals of increase and decrease, solve optimization problems, and analyze connected rates of change.
- OGM.13.CAL.3Open Global Math Standards 2026™ · Math · Level 13 / High School 4 (Age 17–18) · Grade 12Differentiate implicitly defined relations and parametrically defined curves to find first derivatives $\frac{dy}{dx}$.
- OGM.13.CAL.1Open Global Math Standards 2026™ · Math · Level 13 / High School 4 (Age 17–18) · Grade 12Understand differentiation as the limit of a difference quotient and rate of change; differentiate from first principles for integer powers, $\sin x$, and $\cos x$; interpret the derivative as the tangent slope and the second derivative as concavity and inflection points.
Curriculum Framework
12th Grade · Math · Open Global Math
1
7 lessons
Limits, First Principles, and Derivative Foundations
Understand derivatives as limits of difference quotients, differentiate fundamental functions from first principles, and interpret first and second derivatives geometrically.
2
11 lessons
Differentiation Rules and Transcendental Functions
Differentiate power, exponential, logarithmic, and trigonometric functions using product, quotient, chain, and inverse differentiation rules.
3
7 lessons
Implicit Differentiation, Parametric Curves, and Related Rates
Differentiate implicit relations and parametric equations, and solve connected rates of change problems.
4
7 lessons
Applications of Derivatives: Extrema and Optimization
Determine tangent and normal equations, find extrema, analyze curve behavior, and solve real-world optimization problems.
5
8 lessons
Definite Integrals and the Fundamental Theorem of Calculus
Understand integration as the limit of Riemann sums, apply the Fundamental Theorem of Calculus, and integrate standard function families.
6
8 lessons
Advanced Integration Techniques: Substitution, Parts, and Partial Fractions
Master advanced integration methods including u-substitution, integration by parts, and partial fractions for definite and indefinite integrals.
7
6 lessons
Area Under Curves and Between Intersecting Functions
Evaluate definite integrals to calculate the total geometric area under a curve and enclosed between intersecting curves.
8
9 lessons
Differential Equations and Mathematical Modeling
Formulate first-order differential equations from contextual scenarios, find general and particular solutions via separation of variables, and analyze model behavior.