Rates of Change in Applied Contexts (Non-Motion)
General rate-of-change framework
Common applied contexts
Example: population growth
Example: Newton's Law of Cooling
When is the rate of change greatest?
Average rate of change vs instantaneous rate
Interpreting the sign of $f'(x)$
Modeling with piecewise rates
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AP exam tips
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Vocabulary
Unit 4 topics
Unit 4 overview14.1 Interpreting the Meaning of the Derivative in Context24.2 Straight-Line Motion: Position and Velocity34.3 Straight-Line Motion: Acceleration and Speed44.4 Rates of Change in Applied Contexts54.5 Introduction to Related Rates64.6 Setting Up and Solving Related Rates Problems74.7 Advanced Related Rates Problems84.8 Approximating Values Using Local Linearity94.9 Linearization and Differentials104.10 Using L'Hôpital's Rule for Indeterminate Forms