If  $f\left(x\right)=x^3-x^{2}f\text{'}\left(1\right)+x{f}^{\text{'}\text{'}}\left(2\right)-f^{\text{'}\text{'}\text{'}}\left(3\right),x\in R$,  then

Let  $f\left(x\right)=x^3+b{x}^2+cx+d$

$$\begin{gathered} f^1\left(x\right)=3x^2+2bx+c \\ {f}^{11}\left(x\right)=6x+2b \\ {f}^{111}\left(x\right)=6 \end{gathered}$$

Given,  $f\left(x\right)=x^3-x^2{f}^1\left(x\right)+x{f}^{11}\left(2\right)-f^{111}\left(3\right)$

$x^3+b{x}^2+cx+d=x^3-x^2(3+2b+c)+x(12+2b)-6$

By comparing coefficients
- b = 3 + 2b + c           c = 12 + 2b        
-3 = 3b + c ......(1)        2b – c = -12   .......(2)
Eq. (1) & (2)
$$\begin{gathered} 3b+c=-3 \\ 2b-c=-12 \end{gathered}$$

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5b = -15
b = -3, c = 6, d = -6
 $f\left(x\right)=x^3-3x^2+6x-6$
From option 2
2f(0) – f(1) + f(3) = f(2)
2(-6) – (-2) + 12 = 2