Stewart6e4_1 - MATH 191 Sections 1 and 3 Calculus I Fall...

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MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 4.1: Maxima and Minima (And we ain’t talkin’ Nissans. ..) We start off with a load of. .. ...Definitions. We say that the number c is a (or ) for the function f if f ( c ) f ( x ) for all x in f ’s domain. A (or ) is defined analogously: for such c , f ( c ) f ( x ) for all x in f ’s domain. The value f ( c ) is called, respectively, the ( ) for f . Collectively, these numbers and (note the plural forms!) are called ( ) for the function f . It is often easy to find the global , given a graph of the func- tion. More challenging can be finding these points algebraically, straight from a function’s formula. Examples. Where are the global extrema of the function f ( x ) = x 2 ? What value(s) does the function take there? What about for the function f ( x ) = cos( x )?
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More generally, there may be points x = c at which the function attains a maximum or minimum value in a neighborhood of c ; such values of x will be called
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Stewart6e4_1 - MATH 191 Sections 1 and 3 Calculus I Fall...

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