1) у = х³ - 3 х² + 3х,   х₀ = 2

y' = 3x² - 6x + 3,   y'(2) = 12 - 12 + 3 = 3

y(2) = 8 - 12 + 6 = 2

y = 2 + 3(x-2) = 2 + 3x -6 = 3x-4

  Ответ: у = 3х-4

2) у = 3х⁴ - 6х² + 2,   х₀ = -2

y' = 12x³ - 12x,   y'(-2) = -96 + 24 = -72

y(-2) = 48 - 24 + 2 = 26

y = 26 - 72(x+2) = 26 -72x -144 = -72x -118

Ответ: у = -72х - 118

3) у = х³ - 3х + 1,   х₀ = 1

y' = 3x² - 3,   y'(1) = 0

y(1) = 1 - 3 + 1 = -1

y = -1 + 0(x-1) = -1

Ответ: у = -1

Verified answer

1)y=2^3-3*2^2+3*2+(3*2^2-6*2+3)(x-2)=3x-4

2)y=3*(-2)^4-6*(-2)^2+2+(12*(-2)^3-12*(-2))(x+2)=-62x-98

3)y=1^3-3*1+1+(3*1^2-3)(x-1)=-1