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

Answer 1

Answer: 1

$f(x)=\ln \{g(x)\}$
$g(x)=e^{f(x)}$
$g^{′}(x)=e^{f(s)}â‹\dots f^{′}(x)$
$g^{′}(x)=0$
$⇒f^{′}(x)=0$ as $e^{f(s)}î€=0$
$⇒2010(x−2009)(x−2010{)}^2(x−2011{)}^3(x−2012{)}^4=0$
so there is only one point of local maxima.