AP EAMCET · Maths · Application of Derivatives
The maximum value of \(y=x(\log x)^2\) is
- A \(e^{-2}\)
- B \(2 e^{-2}\)
- C \(3 e^{-2}\)
- D \(4 e^{-2}\)
Answer & Solution
Correct Answer
(D) \(4 e^{-2}\)
Step-by-step Solution
Detailed explanation
\(y=x(\log x)^2\) For maximum value \[ \begin{aligned} \frac{d y}{d x} & =x\left(2 \log x \cdot \frac{1}{x}\right)+(\log x)^2 \\ & =2 \log x+(\log x)^2 \end{aligned} \] Now, put \(\frac{d y}{d x}=0\)…
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