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.