Let \( f^{\prime}(x)=\frac{192 x^{3}}{2+\sin ^{4} \pi x} \) for all...

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Let \( f^{\prime}(x)=\frac{192 x^{3}}{2+\sin ^{4} \pi x} \) for all \( x \in R \) with \( f\left(\frac{1}{2}\right)=0 \)
\( \mathrm{P}^{210} \)
W
. if \( m_{\leq} \leq \int_{1 / 2}^{1} f(x) d x \leq M \), then the possible values of \( m \) and \( M \) are
(1) \( m=13, M=24 \)
(2) \( m=\frac{1}{4}, M=\frac{1}{2} \)
(3) \( m=-11, M=0 \)
(4) \( m=1, M=12 \)
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