The number of critical points of \( f(x)=\left(\int_{0}^{x}\left(\cos ^{2} t-\sqrt[3]{t}\right) ...

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The number of critical points of \( f(x)=\left(\int_{0}^{x}\left(\cos ^{2} t-\sqrt[3]{t}\right) d t\right) \) \( +\frac{3}{4} x^{4 / 3}-\frac{x+1}{2} \) in \( [0,6 \pi] \) is
(a) 10
(b) 8
(c) 6
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