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If the tangent to the curve, y = f(x) = x logₑ 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:
- 1/(e - 1)
- e^(1/(1 - e))
- e^(1/(e - 1))
- (e - 1)/e
Correct answer: e^(1/(e - 1))
Solution
The correct option is derived from finding the slope of the tangent to the curve at point (c, f(c)) and equating it to the slope of the line segment joining the points (1, 0) and (e, e). The slope of the line segment is 1, and by differentiating the function and solving for c, we find that c must equal e^(1/(e - 1)}.
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