Unit+4

=Unit 4 Applications of Derivatives=

=Applications of Derivatives=

Unit Overview
In the past, when virtually all graphing was done by hand—often laboriously—derivatives were the key tool used to sketch the graph of a function. Now we can graph a function quickly, and usually correctly, using a grapher. However, confirmation of much of what we see and conclude true from a grapher view must still come from calculus. This chapter shows how to draw conclusions from derivatives about the extreme values of a function and about the general shape of a function's graph. We will also see how a tangent line captures the shape of a curve near the point of tangency, how to deduce rates of change we cannot measure from rates of change we already know, and how to find a function when we know only its first derivative and its value at a single point. The key to recovering functions from derivatives is the Mean Value Theorem, a theorem whose corollaries provide the gateway to integral calculus, which we begin in Chapter 5.

4.3 Connecting f' and f''with the Graph of f


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4.4 Modeling and Optimization


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4.5 Linearization and Newton's Method


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4.6 Related Rates
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