Overestimate or underestimate

This is a valid point. When we made this question last year we intended "near-by" to mean that for points near (1,1) f(x) IS the Taylor polynomial. We then intend that 1.02 is one of these "near-by" points and so the second derivative is always -2 leading to the conclusion from the solution. Technically one should be more rigorous about the error bounds and ensure that 1.02 is close enough to be validated by the Taylor approximation but we decided that was too difficult. Anyway, a solution like what is currently here was a full-marks solution.

Thanks for this clarification Iain. I think that the wording expect, instead of show that, makes it clear enough that the question asks for the intuitive answer, rather than another complicated calculation.