Let \( f \) be a function defined on \( R \) (the set of all real n...

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Let \( f \) be a function defined on \( R \) (the set of all real numbers) such that \( f^{\prime}(x)=2010(x-2009)(x-2010)^{2} \)
\( \mathrm{P} \) \( (x-2011)^{3}(x-2012)^{4}, \forall x \in R \). If \( g \) is a function defined

W. on \( R \) with values in the interval \( (0, \infty) \) such that \( f(x)=\ln (g(x)), \forall x \in R \), then the number of points in \( R \) at which \( g \) has a local maximum is......
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