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Question

Let f be a function defined on R such that
f'(x)=2010(x2009)(x2010)2(x2011)3(x2012)4, for all xR. If g is a function defined on R with values in the interval (0,) such that f(x)=ln(g(x)) for all xR, then the number of points in R at which g has a local maximum is

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Solution

f(x)=ln{g(x)}
g(x)=ef(x)
g(x)=ef(x).f(x)
g(x)=0f(x)=0 as ef(x)0
or 2010(x2009)(x2010)2(x2011)3(x2012)4=0
So there is only one point of local maxima

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