SurCalCh3Sec1 - to negative on the right. The point ( is a...

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3.1—Graphing Using the First Derivative TV, Spring 2001 A function has a relative maximum value at c if for all values of x near c . In other words the point is a peak of the graph. ) ( x f ) ( ) ( x f c f )) ( , ( c f c A function has a relative minimum value at c if for all values of x near c. In other words the point is a valley of the graph. ) ( x f ) ( ) ( x f c f )) ( , ( c f c Examples: A CRITICAL VALLUE of a function is an x-value in the domain of at which the derivative is either zero or undefined. ) ( x f f #6 #14 FACT: Relative extrema occur at CRITICAL VALUES. To determine which critical values are actual extreme values we use: The First Derivative Test If a function has a critical value at x=c then the point ( is a relative maximum if f’ changes from positive on the left of x=c
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Unformatted text preview: to negative on the right. The point ( is a relative minimum if f’ changes from negative on the left of x=c to positive on the right. If the sign of the derivative does not change at x=c then the point ( is neither a max nor a min. )) ( , c f c )) ( , c f c )) ( , c f c To graph by hand (using only the first derivative) 1) Find the x and y intercepts (when possible) 2) Find the critical values and use the first derivative test to determine relative extrema 3) Plot all information on the graph. 4) Connect the dots. #16 Note: Sometimes a function has no critical values. In this case it can have neither max nor min values. To get a graph of such a function we need to plot several additional points....
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This note was uploaded on 01/12/2012 for the course MATH 2043 taught by Professor Pamelasatterfield during the Fall '05 term at NorthWest Arkansas Community College.

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