Срочно решииь только 9 и 10. Created by kobzarenko99. matematika-ru

Срочно решииь только 9 и 10...

nKrynka 9) f(x) =x³ -3x ; g(x) = - 6/x. f'(x) =g'(x) .
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f'(x) =g'(x) ;
(x³ -3x)' = (-6/x) ' ;
3x² -3 = 6/x² ;
x⁴ - x² -2 =0 ;
x₁² = -1 ⇒x∈∅ .
x₂² = 2 ⇔x₂² - 2=0  ⇒x₂,₁* x₂,₂ = - 2.
* * * x₂² = 3 ⇒x₂=±√3 ⇔x₂,₁ = -√3 ; x₂,₂ =√3 ⇒x₂,₁* x₂,₂ = -√3*√3 = -3 * * *
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10) f(x) =(x3+2)/x ; g(x) = 6x +2/x. f'(x) =g'(x) .
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f'(x) =g'(x) ;
((x³+2)/x) ' =(6x +2/x)' ;
(x²+2/x) ' = (6x +2/x)' ;
2x +(2/x) ' =6 +(2/x) ' ;
2x =6 ;
x = 3 .

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oganesbagoyan

Verified answer

Решение
9) f(x) = x³ - 3x
f`(x) = 3x² - 3
g(x) = - 6/x
g`(x) = 6/x²
f`(x) = g`(x)
3x² - 3 = 6/x²
3x⁴ - 3x² - 6 = 0
x⁴ - x² - 2 = 0
x² = t
t² - t - 2 = 0
t₁ = - 1
t₂ = 2
x² = - 1 решений нет
x² = 2
x₁ = - √2
x₂ = √2
x₁ * x₂ = - √2 * √2 = - 2
10) f(x) = (x³ + 2)/x
f`(x) = (3x² * x - x³ - 2)/x² = (2x³ - 2)/x² = 2*(x³ - 1)/x²
g(x) = 6x + 2/x
g`(x) = 6 - 2/x²

2*(x³ - 1)/x² = 6 - 2/x²
(2x³ - 2 - 6x² + 2)/x² = 0
(2x³ - 6x²)/x² = 0
x - 3 = 0
x = 3

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