CLEP Calculus

CLEP Calculus offers students the opportunity to demonstrate their understanding of calculus concepts and applications, enabling them to earn college credit.

Limits and ContinuityDerivatives and Rates of ChangeApplications of Derivatives
Integrals and Area Under CurvesTechniques of IntegrationSequences, Series, and Convergence
Calculus in PhysicsCalculus in Economics and BusinessCalculus in Biology and Medicine
Time Management and PacingProblem-Solving and Test-Taking Tricks
Limits and Continuit...Derivatives and Rate...Applications of Deri...Integrals and Area U...Techniques of Integr...Sequences, Series, a...Calculus in PhysicsCalculus in Economic...Calculus in Biology ...Time Management and ...Problem-Solving and ...
Basic Concepts

Applications of Derivatives

Using Derivatives in the Real World

Derivatives aren’t just abstract math—they help solve real problems! They can find maximum profits, minimum costs, fastest speeds, and points where things change the most.

Common Applications

  • Optimization: Finding the best (maximum or minimum) value for a function, like lowest cost or highest profit.
  • Motion: Calculating velocity and acceleration from position functions.
  • Related Rates: Figuring out how two changing quantities are connected, like how fast a shadow grows as the sun sets.

How to Apply Derivatives

  1. Find the derivative.
  2. Set the derivative equal to zero to find critical points.
  3. Test these points to see if they are maximums, minimums, or points of inflection.

Why It’s Useful

Businesses use derivatives to maximize profits, engineers to design safe roller coasters, and scientists to model changing populations.

Examples

  • A company uses derivatives to figure out the price that gives the most profit.

  • Physics uses derivatives to find the speed of a rocket at any moment.

In a Nutshell

Derivatives help us find where things are fastest, slowest, biggest, or smallest.

Next
Integrals and Area Under Curves