Let be a function defined on such that for all

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

f

be a function defined on

\mathbb{R}

such that

f'(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4

for all

x\in\mathbb{R}

. If

g

is a function defined on

\mathbb{R}

with values in

(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

has a local maximum.