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\( f(x)=\left\{\begin{array}{l}|x-4|, \text { for } x \geq 1 \\ \left(x^{3} / 2\right)-x^{2}+3 x+(1 / 2), \text { for } x=1\end{array}\right. \)
(A) \( f(x) \) is continuous at \( x=1 \) and at \( x=4 \)
(B) \( f(x) \) is differentiable at \( x=4 \)
(C) \( f(x) \) is continuous and differentiable at \( x=1 \)
(D) \( f(x) \) is not continuous at \( x=1 \)
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