2.4 Class Notes - Feb 27 lecture HWK #5 due R 3/8 or F 3/9...

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Feb 27 lecture HWK #5 due R 3/8 or F 3/9 5.3: 36, 42, 50, 68 6.1: 14, 16, 43 6.2: 9, 18, 26 Spring Break March 17-25 Prelim 2: Thursday March 29 Relative Extrema A point c is a relative (or local) maximum for f if there are values a < c < b so that f(c) f(x) for all a x b. -25 -20 -15 -10 -5 0 5 10 15 -3 -2 -1 0 1 2 3 4 5 Critical numbers (p.273) A necessary condition for a point to be a relative or local maximum or minimum is that f (x 0 ) = 0. These points are called critical values . -8 -6 -4 -2 0 2 4 6 8 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Problem Find the x-value of all points where the function f(x) = x 4 -18x 2 has a local extremum. f(x) = x 4 - 18x 2 32 ' () 4 3 6 4( 9 ) 4( 3 ) ( 3 ) critical points 3,0,3 f x x x xx x =−= = + -3 0 3 x+3 — | +++ x— | ++ x - 3 ——— | + f’ + + f(x) = x 4 - 18x 2 -100 -50 0 50 100 150 200 -6 -3 0 3 6
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Problem Find the value of all points x > 0 where the function f(x) = x ln x has a local extremum. f(x) = x ln x 1 ' ( )l n ( 1 /)l n 1 '( ) 0 when 1/ 0 when 1/ 0 when 1/ decreasing then increasing = local min fx xx x x x e e x e x e =+ == = << >> f(x) = x ln x 1/e = .3678 = -f(1/e) -0.4 -0.2 0 0.2 0.4 0.6 00 .
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).

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2.4 Class Notes - Feb 27 lecture HWK #5 due R 3/8 or F 3/9...

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