a) We know that for small values of At we have the expression f (1 ) ~ f (1 + At) - f(1) At Which means that we also have f ( 1 ) = f' (t + At) - f'(t) At Show that from these we obtain an approximation for the double derivative given by f" ( 1 ) = f(1+ 2At) - 2f(1+ At) + f(1) (Ar )2