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Консультация № 174650
28.11.2009, 19:31
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Проведите исследование функции с помощью производной первого порядка и постройте ее график:
f(x)=X в 3 степени - 9 Х во 2 ой степени +24Х +34
f(x)=X в 3 степени - 9 Х во 2 ой степени +24Х +34
Обсуждение
Неизвестный
29.11.2009, 12:34
общий
это ответ
Здравствуйте, Лялюшкин Александр Николаевич.
f(x)=x^3 - 9x^2 + 24x + 34
f'(x)=3x^2 - 18x + 24
f'(x)=0 при х[size=1]1[/size]=2 х[size=1]2[/size]=4 (экстремумы)
При х<2
f'(1)=3-18+24=9>0 - f(x) возрастает
При 2<x<4
f'(3)=3*9-18)3+24=-3<0 - f(x) убывает
При х>4
f'(5)=3*25-18*5+24=9>0 - f(x) возрастает
f(x)=x^3 - 9x^2 + 24x + 34
f'(x)=3x^2 - 18x + 24
f'(x)=0 при х[size=1]1[/size]=2 х[size=1]2[/size]=4 (экстремумы)
При х<2
f'(1)=3-18+24=9>0 - f(x) возрастает
При 2<x<4
f'(3)=3*9-18)3+24=-3<0 - f(x) убывает
При х>4
f'(5)=3*25-18*5+24=9>0 - f(x) возрастает
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