Linearization - no idea how to do this

[donjt81]

Can someone point me in the right direction for this problem. I have no idea how to start on this. I know the linearization formula but i don't know if that's what i have to use here. can someone please help

problem: You want a linearization that will replace the function over an interval that includes the point Xo. To make your subsequent work as simple as possible you want to centre the linearization not at Xo but at a nearby integer X = a at which the function and its derivative are easy to evaluate. find a linearization for the following function. f(x) = x/(x+1), where Xo = 3.8

thanks in advance

 

[Galileo]

You have to linearize the function not at Xo but at a nearby integer, since that's easier to work with. It's clear which integer is close to Xo, so linearize f about that point.