4.3 Rates of Change in Applied Contexts other than Motion
1 min readβ’june 18, 2024
AP Calculus AB/BCΒ βΎοΈ
279Β resourcesSee Units
While the title says βOther Than Motion,β 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.
π 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:
- Distance a car travels
- 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.
π 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
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πUnit 1 β Limits & Continuity
π€Unit 2 β Fundamentals of Differentiation
π€π½Unit 3 β Composite, Implicit, & Inverse Functions
πUnit 4 β Contextual Applications of Differentiation
β¨Unit 5 β Analytical Applications of Differentiation
π₯Unit 6 β Integration & Accumulation of Change
πUnit 7 β Differential Equations
πΆUnit 8 β Applications of Integration
π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
βΎUnit 10 β Infinite Sequences & Series (BC Only)
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