Problem

Problem

Let ff be a function defined on RR (the set of all real numbers) such that f′(x)=2010(x−2009)(x−2010)2(x−2011)3(x−2012)4,∀x∈Rf'(x) = 2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, \forall x \in R . If gg is a function defined on RR with values in the interval (0,∞)(0, \infty) such that f(x)=ln⁡(g(x)),∀x∈Rf(x) = \ln(g(x)), \forall x \in R , then the number of points in RR at which gg has a local maximum is.....

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