Let f be defined by f(x) = x³+1, 1.001+0.03(x-0.1)+0.3(x-0.1)²+2(x-0.1)³, 1.009+0.15(x-0.2)+0.9(x-0.2)²+2(x-0.2)³, 0 ≤ x ≤ 0.1, 0.1 ≤ x ≤ 0.2, 0.2 ≤ x ≤ 0.3. Investigate the continuity of the derivatives of f.