What is the limit of g'(x) on the interval (a, ∞) as x approaches infinity?

[Sethka]

When a question asks along the lines of :
"If a function (g) is decrasing on the interval {x,x)...What would the limg'(x) be (As it approaches infinity)"

What are they looking for? and whatequation am I using? I'm not looking for too much info on how to do, but which direction should I go in? I'm not sure what topic this would lie in.

 

[benorin]

If g(x) is decreasing on the interval, say x\in \[ a,\infty) then, unless you know more about the function g(x), all you can say is \lim_{x\rightarrow\infty}g^{\prime}(x)<0, at least that I can tell.

 

[HallsofIvy]

"decreasing on the interval {x, x)" makes no sense. In any case, it order to talk about a limit at infinity, we would have to know what happens on some unbounded interval, say (a, \infty) as benorin said. And you still can't answer the question except as he said.

For example, if g(x)= ax, with a any negative number, then g'(x)= a for all x and so has limit a. Without more information about g, the limit could be any negative number.