**Unformatted text preview: **. • We will now define derivatives as limits of difference quotients . Derivatives represent slopes of tangent lines (which model or approximate graphs locally) and instantaneous rates of change . • Difference quotients on “small” intervals might be used to approximate derivatives. Conversely, derivatives might be used to approximate marginal change in a function, an idea used in economics. • In calculus, we will use derivatives to help us graph functions by finding where they are increasing , decreasing , or constant . (See Section 1.2.) • Limits, differentiation (the process of taking derivatives), and integration (which reverses differentiation; see Section 9.8) are the three key topics you will find in the first half of a calculus book, and they will be key themes throughout....

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