Задача 58491 ...

604a0f39c87bcc1c7d5253e7

11.03.2021 15:39:03

Решите уравнение f'(x) =0:
f (x) =5x²-3x-1/x-3.

5f3ea7e3faf909182968ddd9

11.03.2021 19:14:29

★

[m]f`(x)=\frac{(5x^2-3x-1)`\cdot (x-3)-(5x^2-3x-1)\cdot (x-3)`}{(x-3)^2}[/m]

[m]f`(x)=\frac{(10x-3)\cdot (x-3)-(5x^2-3x-1)\cdot 1}{(x-3)^2}[/m]

[m]f`(x)=\frac{10x^2-3x-30x+9-5x^2+3x+1}{(x-3)^2}[/m]

[m]f`(x)=\frac{5x^2-30x+10}{(x-3)^2}[/m]


[m]f`(x)=0[/m] ⇒

[m]5x^2-30x+10=0[/m]

[m]x^2-6x+2=0[/m]

D=36-8=28

sqrt(D)=2sqrt(7)

x_(1)=3-sqrt(7); x_(2)=3+sqrt(7)