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Igor171717
@Igor171717
July 2022
2
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Решите производную и определите при каких значениях х она равна 1
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justgoodgirl
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0 votes
Thanks 0
MizoriesKun
x³+x²+16 x³ x² 16
f⁾(x) = (-------------- )⁾ = (------ + --------- + --------)⁾ =(x²+x +16/x)⁾ =
x x x x
0*x - 1*16 16
= 2x²⁻¹ +1 + ----------------- = 2x+1 - -------
x² x²
2x+1- (16/x²) =1
2x*x²- (16/x²) *x²=0
2x³- 16 =0
2x³ =16
x³=8
x=∛8=2
x∛x +3x +18 x∛x 3x 18
f⁾(x) = (---------------------)⁾=(-------- +---------- + --------- )⁾ =
∛x ∛x ∛x ∛x
18 0*∛x - 18* (1/3)*x¹/³⁻¹
= (x + 3∛x² + --------)⁾ =1 +3*(2/3)*x ²/³ ⁻¹ + ------------------------------- =
∛x ∛x²
6 *x⁻²/³ 2 6 2 6
= 1+2*x⁻¹/³ - -------------- = 1+ --------- - ------------- = 1 + ------ - ------- =
∛x² ∛x ∛x² * ∛x² ∛x ∛x⁴
2 6
= 1 + ------- - ---------
∛x x∛x
2 6
1 + ------- - --------- =1
∛x x∛x
2 6
------- - --------- =0
∛x x∛x
2x - 6
------------ =0 ОДЗ х≠0
x∛x
2х-6=0
х=3
2 votes
Thanks 1
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Answers & Comments
f⁾(x) = (-------------- )⁾ = (------ + --------- + --------)⁾ =(x²+x +16/x)⁾ =
x x x x
0*x - 1*16 16
= 2x²⁻¹ +1 + ----------------- = 2x+1 - -------
x² x²
2x+1- (16/x²) =1
2x*x²- (16/x²) *x²=0
2x³- 16 =0
2x³ =16
x³=8
x=∛8=2
x∛x +3x +18 x∛x 3x 18
f⁾(x) = (---------------------)⁾=(-------- +---------- + --------- )⁾ =
∛x ∛x ∛x ∛x
18 0*∛x - 18* (1/3)*x¹/³⁻¹
= (x + 3∛x² + --------)⁾ =1 +3*(2/3)*x ²/³ ⁻¹ + ------------------------------- =
∛x ∛x²
6 *x⁻²/³ 2 6 2 6
= 1+2*x⁻¹/³ - -------------- = 1+ --------- - ------------- = 1 + ------ - ------- =
∛x² ∛x ∛x² * ∛x² ∛x ∛x⁴
2 6
= 1 + ------- - ---------
∛x x∛x
2 6
1 + ------- - --------- =1
∛x x∛x
2 6
------- - --------- =0
∛x x∛x
2x - 6
------------ =0 ОДЗ х≠0
x∛x
2х-6=0
х=3