Calculus
Related Rates worksheets
Differentiate geometric constraints with respect to time and solve unit-aware instantaneous rates.
Preview and downloadCalculus practice
Optimization worksheets
Maximize area or volume under geometric constraints with a complete feasible-domain argument.
Ready-made English PDF · fixed settings
Customization below makes a separate PDF.
Fixed English ready-made files. Custom settings below apply only to the configured PDF.
Ready to print
Start with a ready-made worksheet
State the constraint and feasible domain, differentiate the objective, and justify the global maximum.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetReason from a model
Each worked key keeps the defining constraint, derivative reasoning, exact result, and contextual units together.
Learning objective
What this activity builds
Build a one-variable objective, locate feasible critical points, and prove the global optimum.
Worked example
Why check endpoints?
A critical point alone does not prove a global optimum.
Compare every feasible critical point and endpoint, or use concavity together with endpoint behavior.
Teaching notes
Make the practice count
- Sketch and label the varying dimensions.
- Eliminate one variable before differentiating.
- Report dimensions as well as the objective value.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Configure a deterministic applied-calculus worksheet. Worked answers use the same canonical tasks as the student pages.
Enlarged pages scroll. PDF size stays the same.
A useful next step
Related activities