The temperature in an industrial pasteurization tank is f(x) = x² - 8x + 112 degrees centigrade after x minutes (for 0 ≤ x ≤ 12).
a) Find f'(x) by using the limit definition of a derivative.
b) Use your answer to part a) to find the instataneous rate of change of the temperature after 4 minites. Be sure to interpret the sign of your answer