JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f\,:\,R \to R\) be a function such that \(f\left( x \right) = {x^3} + {x^2}f'\left( 1 \right) + xf''\left( 2 \right) + f'''\left( 3 \right)\), \(x \in R\). Then \(f(2)\) equals
- A \(-4\)
- B \(30\)
- C \(-2\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(-2\)
Step-by-step Solution
Detailed explanation
\(f\left( x \right){x^3} + a{x^2} + bx + c\) \(f'\left( x \right) = 3{x^2} + 2ax + b \Rightarrow c = 6\) \(f''\left( x \right) = 6x + 2a\) \(f'''\left( x \right) = 6\,\,a = f'\left( 1 \right) = 3 + 2a + b\,\,\,\,\, \Rightarrow a + b = - 3\)…
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