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JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f\) be a polynomial function such that \(f(3x)\, = f'(x) , f''(x)\), for all \(x \in R\). Then
- A \(f(2) + f'(2)\,= 28\)
- B \(f''(2) -f'(2)\, = 0\)
- C \(f''(2)-f'(2)\,= 4\)
- D \(f(2) -f'(2) + f''(2)\, = 10\)
Answer & Solution
Correct Answer
(B) \(f''(2) -f'(2)\, = 0\)
Step-by-step Solution
Detailed explanation
Let \(f\left( x \right) = a{x^3} + b{x^2} + cx + d\) \(f\left( {3x} \right) = 27a{x^3} + 9b{x^2} + 3cx + d\) \(f'\left( x \right) = 3a{x^2} + 2bx + c\) \(f''\left( x \right) = 6ax + 2b\) \(f\left( {3x} \right) = f'\left( x \right)f''\left( x \right)\) \(27a = 18{a^2}\)…
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