Local Linearity and Linearization
The local linearity principle
Why this works
The linearization formula
Example 1: approximating $\sqrt{4.1}$
Example 2: approximating $\sin(0.1)$
Example 3: approximating $e^{0.05}$
Common linearizations at $a = 0$
Over-estimate vs under-estimate
Linearization from table data
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