lesson
Curve Sketching with Exponential, Logarithmic, and Trigonometric Functions
Synthesize intercepts, asymptotes, stationary points, and points of inflection to sketch graphs of transcendental functions.
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Applications of Derivatives: Extrema and Optimization
7 lessons
Goal
Determine tangent and normal equations, find extrema, analyze curve behavior, and solve real-world optimization problems.
7 lessons
0 of 7 done
- Equations of Tangents and Normals to Explicit CurvesUp next
- Tangents and Normals to Implicitly Defined CurvesNot started yet
- Intervals of Increase, Decrease, and Local ExtremaNot started yet
- Curve Sketching with Exponential, Logarithmic, and Trigonometric FunctionsYou are here
- Applied Optimization: Geometric Area and Volume ProblemsNot started yet
- Applied Optimization: Economic and Cost Minimization ModelsNot started yet
- Applied Optimization: Distance, Time, and Kinematic ProblemsNot started yet
Learning standards covered
OGM.13.CAL.1Open Global Math Standards 2026™ · 12th GradeUnderstand 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.
OGM.13.CAL.4Open Global Math Standards 2026™ · 12th GradeApply 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.