maxima and minima

hmm.. this is a nice question..
i will try to answer it as much as possible...

f(x)=x/(1+xtanx)
f(x)=1/(1/x+tanx)
let g(x)=1/x+tanx

so the maxima and minima will sort of get reversed..
in the sense that the maximum positive value of f(x) will be the minimum positive value and viceversa...

d/dx[g(x)] = sec^2(x) - 1/x^2
so for max or min of g(x), x=cosx or x=-cosx

this cannot be found directly and we have to use some method of approximation (Newton ralphson if you know it already) to find x... once x is found u can do the double derivative test to find if the point is max or minima..
after that substitute the value of x that you have found. Also you need to find the limiting value of g(x) at 0 and plus and minus infinity. Now you will get the maxima and minima..
if this is not clear ... pls ask again :)
cheers :)