Let \(f:\mathbb{R}\to\mathbb{R}\) be a function such that \(f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)\), \(x\in\mathbb{R}\). Then \(f(2)\) equals -
Show Hint
- 30
- \(-2\)
- \(-4\)
- 8
The Correct Option is B
Solution and Explanation
\(c=6\). \(b=f''(2)=12+2a\). \(a=f'(1)=3+2a+b\Rightarrow a=-3-b\).
Then \(b=12+2(-3-b)=6-2b\Rightarrow b=2,\ a=-5\).
\(f(x)=x^3-5x^2+2x+6\), so \(f(2)=8-20+4+6=-2\).
Answer: (2) \(-2\)
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