Question:medium
The point \(P\) lies on the curve with equation \[ y = x\sqrt{2\log_e(x)}, \qquad x>0. \] If \[ \frac{dy}{dx}=2 \] at \(x=k\), then the value of \(k\) is equal to:
The point \(P\) lies on the curve with equation \[ y = x\sqrt{2\log_e(x)}, \qquad x>0. \] If \[ \frac{dy}{dx}=2 \] at \(x=k\), then the value of \(k\) is equal to:
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The equation \(t + \frac{1}{t} = 2\) always implies \(t = 1\) for real numbers. Recognizing this pattern saves time in solving quadratic equations.
Updated On: Jun 25, 2026
- \(-\sqrt{e}\)
- e
- \(\sqrt{e}\)
- 2e
- \(\frac{e}{2}\)
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The Correct Option is C
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