If the tangent to the curve, $y=f(x)=x \log _e x,(x0)$ at a point $(c, f(c))$ is parallel to the line-segment joining the points $(1,0)$ and $(e, e)$, then $c$ is equal to: [JEE Main 2020, 6 Sep (Shift 2)]

Question

If the tangent to the curve, $y=f(x)=x \log _e x,(x>0)$ at a point $(c, f(c))$ is parallel to the line-segment joining the points $(1,0)$ and $(e, e)$, then $c$ is equal to: [JEE Main 2020, 6 Sep (Shift 2)]

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If the tangent to the curve, \(y=f(x)=x \log _e x,(x>0)\) at a point \((c, f(c))\) is parallel to the line-segment jo…

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