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JEE Advanced 2010Paper 2
Exam
JEE Advanced
Year
2010
Paper
Paper 2
Subject
Mathematics
Chapter
Application of Derivatives

JEE Advanced 2010 · Paper 2 · Mathematics · Application of Derivatives

Let f be a function defined on R (the set of all real numbers) such...

Let ff be a function defined on RR (the set of all real numbers) such that f′(x)=2010(x−2009)f^{\prime}(x)=2010(x-2009) (x−2010)2(x−2011)3(x−2012)4(x-2010)^2(x-2011)^3(x-2012)^4, for all x∈Rx \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))f(x)=\ln (g(x)), for all x∈Rx \in R, then the number of points in RR at which gg has a local maximum is

Correct answer

1

Step-by-step solution

Let g(x)=ef(x),∀x∈Rg(x)=e^{f(x)}, \forall x \in R \Rightarrow g^{\prime}(x)=e^{f(x)} \cdot f^{\prime}(x) ⇒f′(x)\Rightarrow f^{\prime}(x) changes its sign from positive to negative in the neighbourhood of x=2009⇒f(x)x=2009\Rightarrow f(x) has local maxima at x=2009x=2009 So, the number of local maximum is one.
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