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This 5 page Class Notes was uploaded by Goran Notetaker on Tuesday October 13, 2015. The Class Notes belongs to MAT 210 at Arizona State University taught by in Fall 2015. Since its upload, it has received 57 views.
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Date Created: 10/13/15
MAT210 Brief Calculus October 1st Lecture Applications of Derivatives Extrema of f X ab is a Closed interval n relative is maximum ll 395 relative quotii Jr maximum e III l I a n ii 1 1H5 R fElififIT j r I i m m i39a relative 5 5 a 5 minimum abeel 1111 mirrjrinum Critical Points f39lx0 o The interval may include points where f x is undefined sharp turns or cusps Glob marr Not an extreme value Local 1113 Local I39 ELEE Localmjn T nal min Global min Localmjn Local maximums occur when the derivative goes from an increasing to decreasing slope gt 0 Local minimums occur when the derivative goes from a decreasing to increasing slope gt 0 Global minimums are the absolute lowest minimums in the entire interval 0 Global maXimums are the absolute highest maXimums in the entire interval l t laxiiruuii Minimum lill ll3l itur Dianna njj i i 1 ii Jnrn MAT210 Brief Calculus October 1st Lecture Find the exact location of all the relative asbolute extrema of the function f4 x3 12x6with thedomain l 22 Findthe first derivative 12 x2 12 0 12x2 1 0 Set derivative equal 2 0A solve for X 12 0 meaningless x2 1 0 x1x 1O X21 X 2 1 At these X values are critical points f39iai H EEt4xs 39i Fin the Firet derivative ueina i aria e iLvEwEaarJii Jt iMaE ji39 j 1 3v W EH3 4 Eat 4 r Ev LE a E Ea M a 41 eat H ex a v3 K i 233 i 31 fine vequote eatreme when t39ifwi E First Derivative Test First Derivative Test First Derivative Test local and g io bal Suppese that t is a critical number of a continuous imam H maximum function f Jr maximum shquot a If f changes from positive to negative at it then f f it has a local maximum at L v a b If 139 changes from negative to positive at c then f f mkiirg has a lecai minimum at c w I m c If i does net change Sign at c tor example if fquot is positive on betn sides at c at negative on betn Maca sides ti nen t has no iecal maximum er minimum minimum at c H MAT210 Brief Calculus 5 October lst Lecture Emmyle leInsider f in 1 I5 4 whieh he derivelive f i e 1a w 13 i Sinee 3 is the Sentient IE 2a Leter39mine whether this er39jxieel Immher 39E a me JILth er neither ei er where f 39E memesing 311 Ileereesjhg
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