Question

ДАЮ 40 БАЛЛОВ СРОЧНО!!!
f(x) = x³/3 - 2.5x² + 6x - 1 если f'(x)=0

Answer 1

$f(x) = \frac{ {x}^{3} }{3} - 2.5 {x}^{2} + 6x - 1 \\ f'(x) = \frac{3}{3} {x}^{3 - 1} - 2.5 \times 2 {x}^{2 - 1} + 6 {x}^{1 - 1} - 0 = \\ = {x}^{2} - 5x + 6 \\ f'(x) = 0 \\ {x}^{2} - 5x + 6 = 0 \\ a =1\\ b = - 5\\ c =6\\ D =  {b}^{2}  - 4ac = ( - 5) {}^{2} - 4 \times 1 \times 6 = 25 - 24 = 1 \\ x_{1} = \frac{5 - 1}{2} = \frac{4}{2} = 2\\ x_{2} = \frac{5 + 1}{2} = \frac{6}{2} = 3$