2.3 Class Notes - Increasing and decreasing 12 f(x = x3 3x2...

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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( 3)( 1) 1 ( )( ) 1 3 ( )( ) 3 g increasi decreasi ( )( ) g ng n f x x x x x x x x x x = = = + < − = + < < + = − < + + = + f(x) = x 3 – 3x 2 – 9x + 6 -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 3 6 9 has roots 6 36 4 3 ( 9) 6 144 1 2 6 6 b b ac a x x c x bx a ± ± ⋅ − ± = = = + ± + Drug concentration, problem 41 2 The concentration of a drug in the blood strem t hours later 4 ( ) 3 27 When is th increasi is , decr n ? ea ing g s t K t t = + K(t) = 4t/(3t 2 + 27) 2 2 2 2 2 4(3 27) 4 (6 ) '( ) (3 27) numerator = 12 108 0 108 wh increasing en t 9 12 0 d ecreasin 3 g 3 t t t K t t t t t + = + + < > = < >
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