Prove if exists, then where and
is called the linearization of at explain part geometrically by interpreting and graphically.
a) The usual proof for this (at least the one from Spivak's Calculus) uses L'Hopital's rule, but going through it I realized I'm not sure if it's valid if we only assume f'(a) exists (and not that the derivative exists in some neighbourhood of a).
b)Just notice that L is the straight line tangent to f at a.