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I was reading a article about about Hermite interpolation on this link. In cardinal spline curve section they give a formula to calculate tangents at end point given as
$T_i = a ( P_{i+1} - P_{i-1} ) . $

Doubt:if i have two point $P_1$ AND $P_2$ then to find $T_1$
$T_1=a(P_2-P_0)$..i need to calculate this but what should be my $P_0$ point?
similarly to find $T_2$ i will need to KNOW $P_3$

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    For the endpoints in splines, it is customary to either estimate slopes from the data points given (through polynomial extrapolation for instance) or to supply them. From that, the slopes at the inner points are computed. I would suggest getting a better reference for Hermite interpolation/splines than that web page; any decent CG book should give the proper formulae.2011-05-09

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The Wikipedia article suggests not to extend the curve to the end points, and to use them only for calculating the tangents at the adjacent points (see the image).

Since there is effectively one specification missing at each end, another approach would be to lower the degree of the polynomial in the final segments by one, that is, to use the unique quadratic polynomial with the two specified points and the one specified tangent. This corresponds to choosing the tangent of the cubic spline such that the cubic term vanishes, which yields

$T_1=2(P_2-P_1)-T_2\;.$