\( f:[0,1] \rightarrow R \) is defined as \( f(x)=\left\{\begin{arr...

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\( f:[0,1] \rightarrow R \) is defined as
\( f(x)=\left\{\begin{array}{lc}x^{3}(1-x) \sin \left(\frac{1}{x^{2}}\right), & 0x \leq 1 \\ 0, & x=0\end{array}\right. \), then
\( \mathrm{P} \)
(1) \( f \) is continuous but not derivable in \( [0,1] \)
(2) \( f \) is differentiable in \( [0,1] \)
(3) \( f \) is bounded in \( [0,1] \)
(4) \( f^{\prime} \) is bounded in \( (0,1] \)
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