Question

Determine wether the given function has any local or absolute extreme values, and find those values if possible.

f(x) = 1/(x^2 + 1)

Can you please explain how to know if the point is abs max or abs min if I don't think about how the graph of this function looks like.

So I've found out that

f ' (x) = (-2x)/((x^2 + 1))^2 = 0, so x=0 is a critical point.

f(0) = 1.

I know the answer is abs max 1 at x = 0, but why isn't it abs min?

Please explain thoroughly how to know when the abs value is min and when it's max. :)

Answer 1