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Increasing and decreasingf(x) = x2– 2x + 3f′(x) = 2x – 2When f’(x)>0 (x>1) the function is increasingWhen f’(x)<0 (x<1) the function is decreasing024681012-2-101234f(x) = x3– 3x2– 9x + 622increasin'()3693(23)3(3)(1)1 ()()13 ()()3gincreasidecreasi()()gngnfxxxxxxxxxx=−−=−−=−+< −−−= +−<<−+= −<++= +f(x) = x3– 3x2– 9x + 6-25-20-15-10-5051015-3-2-1012345What if you can’t guess the roots?22240 has roots 2369 has roots6364 3 (9)61441266bbacaxxcxbxa−−−±−±−⋅⋅ −±===+±+Drug concentration, problem 412The concentration of a drug in the blood strem t hours later 4( )327When is thincreasiis , decrn?ea inggstK tt=+K(t) = 4t/(3t2+ 27)222224(327)4 (6 )'( )(327)numerator = 121080108whincreasing en t9120decreasin3g 3tttKttttt+−=+−+<>=≤<>
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