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Консультация № 200624
12.04.2021, 00:06
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1
Здравствуйте, уважаемые эксперты! Прошу Вас помочь решить следующую задачу:
Написать уравнение касательной и нормали к кривой y=(x+1)(cbrt (3-x)) (или y = (x + 1) cuberoot(3 - x) ) в точках А (-1;0), В (2;3), С (3;0).
Написать уравнение касательной и нормали к кривой y=(x+1)(cbrt (3-x)) (или y = (x + 1) cuberoot(3 - x) ) в точках А (-1;0), В (2;3), С (3;0).
Обсуждение
12.04.2021, 01:08
общий
это ответ
Здравствуйте, katysha.egorova!
Заметим, что функция проходит через каждую из трех данных точек
Найдем производную функции:
уравнение касательной:
уравнение нормали:
уравнение касательной:
уравнение нормали:
Так как касательная параллельна оси Ох, то нормаль перпендикулярна оси Ох и ее уравнение имеет вид:
производная не существует в точке
, но функция определена в этой точке и производная слева и справа от этой точки имеет один и тот же знак, тогда касательная перпендикулярна оси Ох и имеет вид
уравнение нормали:
Так как касательная перпендикулярна оси Ох, то нормаль паралельна оси Ох и ее уравнение имеет вид:
(в данном случае совпадает с осью Ох)
Заметим, что функция проходит через каждую из трех данных точек
Найдем производную функции:
уравнение касательной:
уравнение нормали:
уравнение касательной:
уравнение нормали:
Так как касательная параллельна оси Ох, то нормаль перпендикулярна оси Ох и ее уравнение имеет вид:
производная не существует в точке
, но функция определена в этой точке и производная слева и справа от этой точки имеет один и тот же знак, тогда касательная перпендикулярна оси Ох и имеет вид уравнение нормали:
Так как касательная перпендикулярна оси Ох, то нормаль паралельна оси Ох и ее уравнение имеет вид:
(в данном случае совпадает с осью Ох)
5
Благодарю Вас за помощь! Лучший ответ!
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