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 wi

Question

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 ) = ln ( g ( x )) , for all x ∈ R , then the number of points in R at which g has a local maximum is

TestHub · Accepted Answer

Let g ( x ) = e f ( x ) , ∀ x ∈ R ⇒ g ′ ( x ) = e f ( x ) ⋅ f ′ ( x ) ⇒ f ′ ( x ) changes its sign from positive to negative in the neighbourhood of x = 2009 ⇒ f ( x ) has local maxima at x = 2009 So, the number of local maximum is one.

Mathematics - Application of Derivative Question with Solution | TestHub

Doubts & Discussion

JEE Advanced (2028)