Use first- and second-derivative sign analysis to find critical numbers, determine intervals of increase and decrease, classify local extrema, and identify concavity and points of inflection. Use derivative information to write tangent and normal line equations and sketch standard polynomial, rational, exponential, logarithmic, and trigonometric curves using intercepts, domain restrictions, end behavior, and asymptotes where appropriate. Model and solve single-variable optimization and related-rates problems by applying derivative tests, endpoint analysis, implicit differentiation, constraints, feasible domains, units, and contextual interpretation.
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- Master skills like “Find critical numbers”, “Solve optimization problems”, and “Sketch curves using derivative information” with unlimited, free practice problems
- Download (or modify) free worksheets on Applications of Derivatives you can use at home or in class with practice problems across all skills in this group including “Determine intervals of increase and decrease”, “Determine concavity using the second derivative”, “Classify local extrema using the first derivative”.
- Start working on adaptive units like “Derivatives and Critical Points - Intro” or “Slopes and Perpendiculars - Practice” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Applications of Derivatives: Individual Skills
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Practice 'Classify local extrema using the first derivative'
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Download/Modify Free Grade 12 'Applications of Derivatives' Worksheet
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This Worksheet Includes:
- Classify local extrema using the first derivative
- Determine concavity using the second derivative
- Determine intervals of increase and decrease
- Find critical numbers
- Sketch curves using derivative information
- Solve optimization problems
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Applications of Derivatives) through scaffolded problems that grow in difficulty as concepts are understood.