$f(x)=x^3-x^2f'(1)+xf''(2)-f'''(3)$, $x\in\mathbb{R}$. Then which of the following is incorrect?
Step-by-Step Solution
Key Concept: Let $f'(1)=a$, $f''(2)=b$, $f'''(3)=c$; differentiate to find $a,b,c$
$f'''(3)=6=c$. $f''(2)=12-2a=b$. $f'(1)=3-2a+b=a\Rightarrow 3-3a+12-2a=a\Rightarrow a=3$. $b=6$. $f(0)=-b=-6$ (wait: $f(0)=0-0+0-c=-6$). $f'(3)=27-6+6=27\ne 10$. So $f'(3)=10$ is incorrect.
Correct Answer: 2