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.