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3.9 – Related Rates

3.9 – Related Rates. The Idea. If one quantity is changing in an equation or situation at a particular moment, how much is another quantity changing? Example : As you blow up a balloon, what quantities are changing?. What You Do. Read the problem and understand what is being asked.

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3.9 – Related Rates

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  1. 3.9 – Related Rates

  2. The Idea If one quantity is changing in an equation or situation at a particular moment, how much is another quantity changing? Example: As you blow up a balloon, what quantities are changing?

  3. What You Do • Read the problem and understand what is being asked. • Consider the GENERAL case first. • 2. Draw a diagram and assign variables for the situation. • 3. Create an equation that models the situation at any time in the situation, not just the one given.

  4. What You Do • 4. Use implicit differentiation and differentiate each variable with respect to yet another variable (usually time). • Solve for the rate desired in the question. • Now Consider the SPECIFIC Situation • 6. Plug in the specific quantities given to answer the questions.

  5. Example Let x, y, and z, be some unknown functions of time t, where x2 + y2 = z2. If dx/dt = -3, dz/dt = 5, determine dy/dt when x = 2 and z = 5. If x, y, and z are measured in meters and t is measured in seconds, what are the units on dy/dt?

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