Let `f` be a function defined on `R` (the set of all real numbers) such that `f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4,` for all `x in Rdot` If `g` is a function defined on `R` with values in the interval `(0,oo)` such that `f(x)=ln(g(x)),` for all `x in R ,` then the number of point is `R` at which `g` has a local maximum is ___

Answer

1

Explanation

`f(x)=ln {g(x)}`
`therefore g(X)=e^(f(x))`
`therefore g(x)=e^(f(x)).f(x)`
`g(X)=0 rarr f(x)=0` as `e^(f(x)) ne 0`
or `2010(x-2009)(x-2010)^(3)(x-2012)^(4)=0`
So there is only one point of local maxima