Calculus I (MATH 101) Applications of Derivatives Practice Problems (Optimization, Related Rates, Curve Sketching)
Stanford University
Calculus I (MATH 101) | Practice Problems

Overview
A Calculus I finals packet for application-of-derivatives questions: set up optimization cleanly, do related rates with units, and sketch curves using first/second derivative tests.

Key topics
•optimization workflow (variables, constraint, objective)
•related rates diagrams and chain rule with time
•critical points and intervals for increasing/decreasing
•concavity and inflection points
•linearization and interpreting tangent-line approximations

Suggested study tasks
•solve 10 optimization problems (each with a setup checklist)
•solve 10 related-rates problems with diagrams
•do a curve-sketching drill on 8 functions (sign charts)
•compute 8 linear approximations and estimate error direction
•write a one-page template for setting up word problems

Common pitfalls
•forgetting to define variables and constraint
•differentiating before substituting variables
•dropping units in related rates
•missing endpoints in optimization on intervals
•mixing up concavity vs increasing