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:

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:

Accepted Answer

Correct answer: D. (d) JEE Main 2020 ∵y=x log_e ⁡x (x>0 ) ⇒ dy dx=1+ log_e ⁡x ⇒ dy dx ]_x=c=1+ log_e ⁡c (slope) ∵ The tangent is parallel to line joining (1 ,0 ) , (e ,e ) So 1+ log_e ⁡c= e-0e-1 log_e ⁡c= ee-1-1 ⇒ log_e ⁡c= 1e-1 c=e^ 1e-1

$If the tangent to the curve, y = f (x) = x log_{e} x, (x > 0) at a point (c, f (c)) is parallel to the line- segment joining the points (1, 0) and (e, e), then c is equal to:$

Solution

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