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4.3 Rates of Change in Applied Contexts other than Motion

1 min readβ€’june 8, 2020

AP Calculus AB/BC ♾️

279Β resources
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While the title says β€œOther Than Motion,” really all rates of change are talking about something being in motion. It may not directly say something is in motion but is talking about a change in some way that involved something moving.

πŸ” Examples

Here are some examples, as an activity, think of the units of the first and second derivatives of these situations.Β 
1. A population of rabbits and how many are there each year.
  • 1st derivative: rabbits/year
  • 2nd derivative: rabbits/year squared.Β 
2. Liters of Gas filling a tank and how long it takes in hours.Β 
  • 1st derivative: liters/hour
  • 2nd derivative: liters/hour squared.Β 
You probably get the point!
  • 1st derivative: Measure/time
  • 2nd derivative: Measure/time squared.
Some other situations to apply the rate of change to:
  1. Distance a car travels
  2. People or objects entering or leaving a place
In all these situations, you can use the context to see if the derivative should be positive or negative.Β 
For example, If people are leaving a room, their rate of change would be negative.

πŸ““ Practice

What situations would make the rates of change of the other three situations negative?
  • Rabbits: Population declining (SAD MEME)
  • Liters of Gas: Gas being used and leaving the tank
  • The distance a car travels: Car turns around back to where it came
Browse Study Guides By Unit
πŸ‘‘Unit 1 – Limits & Continuity
πŸ€“Unit 2 – Fundamentals of Differentiation
πŸ€™πŸ½Unit 3 – Composite, Implicit, & Inverse Functions
πŸ‘€Unit 4 – Contextual Applications of Differentiation
✨Unit 5 – Analytical Applications of Differentiation
πŸ”₯Unit 6 – Integration & Accumulation of Change
πŸ’ŽUnit 7 – Differential Equations
🐢Unit 8 – Applications of Integration
πŸ¦–Unit 9 – Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
β™ΎUnit 10 – Infinite Sequences & Series (BC Only)
🧐Multiple Choice Questions (MCQ)
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πŸ“†Big Reviews: Finals & Exam Prep

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