AP EAMCET · Maths · Application of Derivatives
If the normal drawn at the point \(P\) on the curve \(y=x \log x\) is parallel to the line \(2 x-2 y=3\), then \(P=\)
- A \((\mathrm{e}, \mathrm{e})\)
- B \(\left(\frac{1}{\mathrm{e}}, \frac{-1}{\mathrm{e}}\right)\)
- C \(\left(\frac{1}{\mathrm{e}^2}, \frac{-2}{\mathrm{e}^2}\right)\)
- D \(\left(e^3, 3 e^3\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{1}{\mathrm{e}^2}, \frac{-2}{\mathrm{e}^2}\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \log x + x \cdot \frac{1}{x} = \log x + 1\) Slope of normal \(m_n = -\frac{1}{\log x + 1}\) Slope of line \(2x - 2y = 3\) is \(m_l = 1\) \(m_n = m_l \Rightarrow -\frac{1}{\log x + 1} = 1\)…
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