Related rates

Definition

Related rates are equations that relate the rates at which two or more related variables change over time. They are typically used to solve problems involving real-world scenarios where multiple quantities are changing simultaneously.

5 Must Know Facts For Your Next Test

1. To solve a related rates problem, you often start by writing an equation that relates the variables of interest and then differentiate implicitly with respect to time.
2. The chain rule is essential in solving related rates problems because it allows you to differentiate composite functions with respect to time.
3. Identifying which quantities are constant and which are changing is crucial for setting up your related rates equation correctly.
4. Units must be consistent when working with related rates; mixing units can lead to incorrect solutions.
5. Problems often involve geometric relationships like those in circles, spheres, and right triangles.

Review Questions

• How do you use implicit differentiation in solving a related rates problem?
• Why is the chain rule important in solving related rates problems?
• What steps should you follow to set up a related rates problem?

Related terms

Implicit Differentiation: A technique used to differentiate equations that define one variable implicitly in terms of another.

Chain Rule: A formula for computing the derivative of the composition of two or more functions.

Geometric Relationships: Mathematical relationships involving shapes and figures, such as those found in circles, spheres, and triangles.