CUET · MATHS · PYQ PAPER 2025
If \(f(x)=x^3 \log _e x\), Then \(f^{\prime \prime}\left(e^2\right)\) is equal to
- A \(5 e^4+12 e^2\)
- B \(17 e^2\)
- C \(12 e^4+5 e^2\)
- D \(17 e^4\)
Answer & Solution
Correct Answer
(B) \(17 e^2\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{d}{dx}(x^3 \ln x) = 3x^2 \ln x + x^3 \cdot \frac{1}{x} = 3x^2 \ln x + x^2\) \(f''(x) = \frac{d}{dx}(3x^2 \ln x + x^2) = (6x \ln x + 3x^2 \cdot \frac{1}{x}) + 2x = 6x \ln x + 3x + 2x = 6x \ln x + 5x\)…
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