If \( f(x)=x^{4}(1-x)^{2} \) then which of the following is(are) correct?....

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If \( f(x)=x^{4}(1-x)^{2} \) then which of the following
\( \mathrm{P} \)
is(are) correct?
W
(1) \( f^{\prime}(c)=0 \) for some \( c \in(0,1) \)
(2) \( f^{\prime \prime}(x) \) vanishes exactly twice in \( R \)
(3) \( f(x) \) is an even function
(4) Monotonic increasing in \( \left(0, \frac{2}{3}\right) \cup(1, \infty) \)


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