A function \( f \) is differentiable in the interval \( 0 \leq x \leq 5 \) such that \( f(0)=4 \...

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A function \( f \) is differentiable in the interval \( 0 \leq x \leq 5 \) such that \( f(0)=4 \) and \( f(5)=-1 \). If \( g(x)=\frac{f(x)}{x+1} \), then there exists some \( c \in(0,5) \) such that \( g^{\prime}(c)= \)
(A) \( -\frac{1}{6} \)
(B) \( -\frac{5}{6} \)
(C) \( \frac{1}{6} \)
(D) \( \frac{5}{6} \)
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