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Solving Related Rates Problems

Samuel Baker

Samuel Baker

7 min read

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Study Guide Overview

This study guide covers related rates problems in AP Calculus. It reviews the basic concepts of related rates, provides a step-by-step approach to solving these problems (including implicit differentiation), and offers practice problems involving scenarios like an expanding rectangle and a sliding ladder. The guide emphasizes interpreting problem statements, drawing diagrams, setting up equations, and solving for desired rates of change.

Welcome back to AP Calculus with Fiveable! In this session, we're diving into the world of related rates. Get ready to apply your calculus skills to real-world scenarios and solve problems that involve the rates at which quantities change with respect to time. 🕰️

🔗 Related Rates Basics

Related rates problems involve finding the rate at which a variable changes concerning the rate of change of another related variable. These scenarios may involve geometric figures and equations that connect different variables to time.

To review related rates, check out the previous Fiveable guide: Introduction to Related Rates.

🪜 Steps to Solve Related Rates Problems

When you first look at a related rates problem, you will be presented with so much information that you may feel overwhelmed. It’s okay to take a step back and organize before solving anything out!

The following steps will help you manage a related rates problem efficiently.

  1. 📚 Read the Problem Carefully: Identify values that are significant to the problem. You may find it helpful to circle, underline, or rewrite these values off to the side.
  2. ✏️ Draw a Diagram: Visualizing the situation by drawing a diagram can help us understand how each of the variables are changing. Make sure to accurately label variables and indicate their rates of change.
  3. 🏁 Set up an Equation: Use the information given to set up an equation that relates the variables involved. Usually, these equations are geometric, or given.
  4. 💫 Implicit Differentiation: Differentiate the equation implicitly with respect to time (t). This usually involves applying the chain rule to ea...