Stewart6e2_8 - MATH 191 Sections 1 and 3 Calculus I Fall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 2.8: The Derivative, as a Function Now let’s do what I know you’ve been itchin’ to do for the last few classes. Notice that f gives us a rule for assigning, to any given number a , a new value in the set of real numbers. That is, f is really a . Let’s just change the “ a ” in our formula to an “ x ” so we can write f in a more familiar “functional” notation: Definition. We define the derivative of f ( x ) to be the function f whose value at x is given by f ( x ) = lim h → f ( x + h )- f ( x ) h when this limit exists. Because we know how to interpret f ( a ) at any point a , we can sketch a graph of f , even if we have only a graph (and no formula!) for f ( x )! Just use the following simple principles: 1. f ( x ) = 0 whenever the tangent to f ( x )’s graph is horizontal! 2. Where does f ( x ) get its steepest, with both negative and positive slope?...
View Full Document

This note was uploaded on 04/08/2008 for the course MATH 191 taught by Professor Bahls during the Fall '07 term at UNC Asheville.

Page1 / 3

Stewart6e2_8 - MATH 191 Sections 1 and 3 Calculus I Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online