Предмет: Математика, автор: crazy2212

Найти промежутки выпуклости и точки перегиба кривой y=x^3-12x^2+1

Ответы

Автор ответа: mgdev7752

Ответ:

Алгоритм:

а)взять первую производную

б) вычислить значения х, при которых первая производная равна 0

в) вычислить вторую производную и её знаки при значения х которые получили в пункте(б)

г) исследовать поведение второй производной в этих точках.

Итак:

первая производная: 3х²-24х

3х²-24х=0 при х=0 и х=8

вторая производная: 6х-24 при х=0 меньше 0, а это значит, что функция у(максимум)(т.е выпуклость)=1 при х=0

6х-24 при х=8 больше 0, а это значит, что функция у(минимум)(т.е вогнутость)=-255(но нас это по условию задачи не интересует)

Удачи!

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