IIT JEE Advanced 2007 Paper 1

Let A(c – 1, ec–1), B(c + 1, ec+1) and P(c, ec) be three points on the curve. Now, if the slope of AB is greater than slope of tangent at P, then the point of intersection of AB and the tangent lies left to point P.
Slope of tangent at P = ec.
Slope of line AB is

ex+1−ec−1

(x+1)(−(c−1)

= ec

(e−e−1)

2

= ec(

e2−1

2e

)
Since

e2−1

2e

> 1, we get
ec(

e21

2e

) > ec
which implies that the point of intersection lies left to point.