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If the tangent to the curve , y =f (...

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

A

`(e-1)/(e)`

B

`""_(e)((1)/(e-1))`

C

`""_(e)((1)/(1-e))`

D

`(1)/(e-1)`

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