Question

найдите значение производной функции f(x) в точке х0
4) f(x) = (2x – 1)(х + 3) - x, x0 = 1 1/3​

Answer 1

Ответ:

$f(x) = (2x - 1)(x + 3) - x \\ f(x) = 2 {x}^{2} + 6x - x - 3 - x \\ f(x) = 2 {x}^{2} +4x - 3$

$f'(x) = 4x + 4$

$x_{0} = 1 \frac{1}{3} = \frac{4}{3}$

$f'(x_{0}) = 4 \times \frac{4}{3} + 4 = \frac{16}{3} + \frac{12}{3} = \frac{28}{3} = 9 \frac{1}{3}$