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Application of Derivatives question

2010 · Shift 2 · Q22

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JEE Advanced
Mathematics
Application of Derivatives
2010 · Shift 2 · Q22

Application of Derivatives question

2010 · Shift 2 · Q22

JEE AdvancedMathematicsApplication of DerivativesNumerical+4 / −1

Let

f

be a function defined on

R

(the set of all real numbers) such that

f'\left( x \right) = 2010\left( {x - 2009} \right){\left( {x - 2010} \right)^2}{\left( {x - 2011} \right)^3}{\left( {x - 2012} \right)^4}

for all

x \in R

If

g

is a function defined on

R

with values in the interval

\left( {0,\infty } \right)

such that

f\left( x \right) = ln\,\left( {g\left( x \right)} \right),\,\,for\,\,all\,\,x \in R

then the number of points in

R

at which

g

has a local maximum is

\underline{\hspace{2cm}}

.

Numerical answer

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