Related Rates & Optimization Calculator
How fast is the ladder sliding? What box holds the most? Related rates link changing quantities through implicit differentiation; optimization turns a constraint into a max-or-min hunt with the derivative tests.
1 Related-rates solver
Pick a classic scenario, enter the known values, and get the full relate → differentiate → substitute → answer chain.
Steps
Choose a scenario and press Solve.
2 The method, always
- Relate: geometry first — write the equation connecting the quantities.
- Differentiate: with respect to time t; every variable earns its rate factor.
- Substitute: plug in the known values after differentiating.
- Answer: with units, and let the sign tell the story (negative = decreasing).