If the function $$e^{-x} f(x)$$ assumes its minimum in the interval [0, 1] at $$x = \frac{1}{4}$$ which of the following is true ?

A

$$f'(x) < f(x), \frac{1}{4} < x < \frac{3}{4}$$

B

$$f'(x) > f(x), 0 < x < \frac{1}{4}$$

C

$$f'(x) < f(x), 0 < x < \frac{1}{4}$$

D

$$f'(x) < f(x), \frac{3}{4} < x < 1$$