Chapter 3: Applications of Differentiation
Section 3.1 - Tangent and Normal Lines
Section 3.2 - Newton's Method
Section 3.3 - Taylor Polynomials
Section 3.4 - Differentials and the Linear Approximation
Section 3.5 - Curvature of a Plane Curve
Section 3.6 - Related Rates
Section 3.7 - What Derivatives Reveal about Graphs
Section 3.8 - Optimizations
Section 3.9 - Indeterminate Forms and L'Hôpital's Rule
Section 3.10 - Antiderivatives
The calculus has survived the test of time because it has proved to be both practical and useful. The derivative quantizes how one quantity varies when a related quantity changes. The sections in Chapter 3 cover different applications of the derivative, some geometric, some physical, some analytical. There are many other fields and applications - biology, finance, etc., that could have appeared in Chapter 3. But with a solid foundation in the meaning of the derivative, and exposure to a handful of applications, it should be possible to interpret any number of other applications in more diverse fields of study.
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