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\[
f(x)=\left\{\begin{array}{cl}
|x-4| & \text { for } x \geq 1 \\
\left(x^{3} / 2\right)-x^{2}+3 x+1 / 2 & \text { for } x1
\end{array}\right. \text { then }
\]
(a) \( f(x) \) is continuous at \( x=1 \) and \( x=4 \)
(b) \( f(x) \) is differentiable at \( x=4 \)
(c) \( f(x) \) is continuous and differentiable at \( x=1 \)
(d) \( f(x) \) is only continuous at \( x=1 \)
\( \mathrm{P} \)
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