Let \( F(x)=\int_{x^{2}}^{x^{3}} \frac{d t}{\log t}, x0 \). then (a) \( f^{\prime}(x)=-1 / 6 \lo...

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Let \( F(x)=\int_{x^{2}}^{x^{3}} \frac{d t}{\log t}, x0 \). then
(a) \( f^{\prime}(x)=-1 / 6 \log x \)
(b) \( f \) is an increasing function
(c) \( f \) has minimum at \( x=1 \)
(d) \( f \) is an increasing function on \( (1, \infty) \)
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