If \( \mathrm{f}(\mathrm{x}) \) is continuous in \( [a, b] \) differentiable in \( (a, b) \) and...

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If \( \mathrm{f}(\mathrm{x}) \) is continuous in \( [a, b] \) differentiable in \( (a, b) \) and \( c \in \) \( (a, b) \) then \( \frac{f(b)-f(a)}{b^{3}-a^{3}} \) equals
(a) \( 3 c^{2} \cdot f^{\prime}(c) \)
(b) \( \frac{f^{\prime}(c)}{3 c^{2}} \)
(c) \( f(c) \cdot f^{\prime}(c) \)
(d) \( 3 c^{2} f(c) \cdot f^{\prime}(c) \)
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