# Points of Maxima

Calculus Level 4

Let $$f(x)$$ be a function defined on $$\mathbb R$$ (the set of all real numbers) such that $f'(x)=2010 (x-2009)(x-2010)^2(x-2011)^3(x-2014)^4$ for all $$x\in\mathbb R$$.

If $$g(x)$$ is a function defined on $$\mathbb R$$ with values in the interval $$(0,\infty)$$ such that $$f(x)=\ln (g(x))$$ for all $$x\in \mathbb R$$, then find the number of points in $$\mathbb R$$ at which $$g(x)$$ has a local maximum.

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