A) \[-4\]
B) 30
C) \[-2\]
D) 8
Correct Answer: C
Solution :
\[f(x)={{x}^{3}}+a{{x}^{2}}+bx+c\] |
\[f'(x)=3{{x}^{2}}+2ax+b\] |
\[f''(x)=6x+2a\] |
\[f'''(x)=6a=f'(1)=3+2a+b\] |
\[\Rightarrow \] \[a+b=-3\] |
\[b=f''=12+2a\] |
\[\Rightarrow \] \[2a-b=-12\] |
\[c=f'''(3)\] |
\[\Rightarrow \] \[c=6\] |
and \[a=-5,b=2\] |
\[\Rightarrow \] \[f(x)={{x}^{2}}-5{{x}^{2}}+2x+6\] |
\[\Rightarrow \] \[f(2)=8-20+4+6=-2\] |
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