2.3 Class Notes - Increasing and decreasing 12 f(x) = x3...

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Increasing and decreasing f(x) = x 2 –2x±+ ±3 f (x) = 2x – 2 When f’(x)>0 (x>1) the function is increasing When f’(x)<0 (x<1) the function is decreasing 0 2 4 6 8 10 12 -2 -1 0 1 2 3 4 f(x) = x 3 –3x 2 –9x ±+±6 2 2 increasin '( ) 3 6 9 3( 2 3) 3)( 1) 1 ( )( ) 1 3 3 g increasi decreasi () g ng n fx x x xx x x x x x =− = + <− − − =+ −< < −+=− <+ + = + f(x) = x 3 2 -25 -20 -15 -10 -5 0 5 10 15 -3 -2 -1 0 1 2 3 4 5 What if you can’t guess the roots? 2 2 2 4 0 has roots 2 36 9 h a s r o o t s 63 6 4 3 ( 9 ) 6 144 12 66 bb a c a x xc x bx a −− −± ±− ± = = = + ± + Drug concentration, problem 41 2 The concentration of a drug in the blood strem t hours later 4 32 7 When is th increasi is , decr n ? ea ing g s t Kt t = + K(t) = 4t/(3t 2 + 27) 2 22 2 2 4 (3 27 ) 4(6) '( ) 27) numerator = 108 0 wh increasing en t 9 0 d ecreasin 3 g 3 tt t t t t t +− = + −+ < >= ≤< >
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K(t) = 4t/(3t 2 + 27) 0 0.05 0.1 0.15 0.2 0.25 03691 2 1 5 Problem 27 2/3 5/3 1/3 () '( ) (2 / 3) (5 / 3) ( increasing /3)(2 5 ) decreasin 2/5 2 5 g / fx x x fx x x xx x x =− < > x 2/3 -x 5/3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 00 . 2 0 . 4 0 . 6 0 .
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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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2.3 Class Notes - Increasing and decreasing 12 f(x) = x3...

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