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Sobaka8906
@Sobaka8906
July 2022
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решите,пожалуйста)))))
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Удачник66
1) Точки перегиба это точки_ в которых производная 2 порядка равна 0.
y=x^3-12x^2+3x
y'=3x^2-24x+3
y''=6x-24=0
x=4; y(4)=64-12*16+3*4=64-192+12=-116
2) y=(x^4+x^2)/(x+2)
y'=[(4x^3+2x)(x+2)-(x^4+x^2)*1]/(x+2)^2=
=(4x^4+2x^2+8x^3+4x-x^4-x^2)/(x+2)^2=
=(3x^4+8x^3+x^2+4x)/(x+2)^2
3) y=x^3*ln x
y'=3x^2*ln x+x^3/x=3x^2*ln x+x^2
y''=6x*ln x+3x^2/x+2x=6x*ln x+5x
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Answers & Comments
y=x^3-12x^2+3x
y'=3x^2-24x+3
y''=6x-24=0
x=4; y(4)=64-12*16+3*4=64-192+12=-116
2) y=(x^4+x^2)/(x+2)
y'=[(4x^3+2x)(x+2)-(x^4+x^2)*1]/(x+2)^2=
=(4x^4+2x^2+8x^3+4x-x^4-x^2)/(x+2)^2=
=(3x^4+8x^3+x^2+4x)/(x+2)^2
3) y=x^3*ln x
y'=3x^2*ln x+x^3/x=3x^2*ln x+x^2
y''=6x*ln x+3x^2/x+2x=6x*ln x+5x