I just want someone to check my derivatives to see if I did them right:

$\displaystyle f(x) = \frac{(ax+b)}{(x-1)(x-4)}$

$\displaystyle f'(x) = \frac{(ax+b)(2x-5)-a(x-4)(x-1)}{((x-1)(x-4))^2}$

$\displaystyle f''(x) = \frac{(ax+b)}{-(2x-5)^3(x^2-5x+4)^2}$