Предмет: Алгебра, автор: jwj9r9xp6m

Розв'яжіть рівняння cos2x = -1
6.Знайдіть значення кутового коефіцієнта дотичної, проведеної до графіка функції f( x) = x3- 2x в точці з абсцисою х0 = 1

Ответы

Автор ответа: FaerVator
1

Ответ:

\displaystyle \boldsymbol{ x =  \frac{ \pi}{2}  +  \pi n,n  \in  \Z}

6. k = 1

Объяснение:

 \cos2x =  - 1 \\ 2x =  \pi + 2 \pi  n,n \in \Z |:2 \\ \boldsymbol{ x =  \frac{ \pi}{2}  +  \pi n,n  \in  \Z}

6.Знайдіть значення кутового коефіцієнта дотичної, проведеної до графіка функції f(x) = x³- 2x в точці з абсцисою х = 1

f(x) = x {}^{3}  - 2x

Найдём производную функции :

f'(x) = \left(x {}^{3} \right )' - 2 \cdot \left(x \right)' \\ f'(x) = 3x {}^{3 - 1}  - 2 \cdot1 = 3x {}^{2}  - 2

Найдём значение производной в точке x :

 f'(1) = 3 \cdot 1 {}^{2}  - 2 = 1

k = f'(x) = 1

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