Let f be a function defined on R (the set of all real numbers) such that
f ′ (x) = 2010 (x – 2009) (x – 2010) 2 (x – 2011) 3 (x – 2012) 4 , for all x ∈ R .
If g is a function defined on R with values in the interval (0, ∞ ) such that f(x) = n (g(x)), for all x ∈ R , then the number of points in R at which g has a local maximum is
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Sol. f ′ (x) = 2010 (x – 2009) (x – 2010) 2 (x – 2011) 3 (x – 2012) 4
f(x) = n (g(x))
⇒ g(x) = e f(x) 
⇒ g ′ (x) = e f(x) . f ′ (x)
only point of maxima [Applying first derivative test]
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