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section35_material - Section 3.5 Derivatives Numerical and...

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MATH 110 BUSINESS CALCULUS CHAPTER 3 INTRODUCTION TO THE DERIVATIVE Section 3.5 Derivatives: Numerical and Graphical Viewpoints The instantaneous rate of change of f(x) at x = a is defined as 0 ( ) ( ) ( ) lim h f a h f a f a h + = [We say “ f prime of a equals the limit as h approaches 0, of the ratio ( ) ( ) f a h f a h + ”] ( ) f a is also called the derivative of f(x) at x = a. Differentiation is the process of finding the derivative. Leibniz d Notation: 0 0 ( ) ( ) ( ) lim lim h h f x h f x f df f x h x dx + Δ = = = Δ Thus, ( ) can be written as in Leibniz Notation x a df f a dx = The vertical line indicates that the derivative is being evaluated at x = a.
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