題組內容

II. (50 points) Fill in the following blanks.

2. Suppose that \( f \) is a continuous function satisfying \( f(x) = x \int_{0}^{x} f(t) dt + x^{3} \) for all \( x \), and \( c \) is a real number such that \( f(c) = 1 \). Then, expressing \( f'(c) \) in terms of \( c \) only is __________(2)__________.