Calculus problem

Question

Given the function 𝑔(𝑥) =(2𝑥)/(1+𝑥^2)

Part 1: Find critical points and possible inflection points.

Part 2: Find intervals on which the function is increasing/decreasing and

concave up / down.

Part 3: Identify extreme values and inflection points.

Part 4: Locate all asymptotes and determine end behavior.

Part 5: Determine the (𝑥, 𝑦) ordered pairs of any x-intercept(s) and any y-intercept of the function, if they exist.

Answer 1

In today's world the easiest way to examine this question is with a graph.

You can then support your answer with whatever algebra and calculus you need.

And if you are worried that you need to know the answers without a graphing calculator, sketch it.

Anyway, it has a zero at the origin, obviously, is asymptotic to 0 from above to the right and from below to the left, and the min is at -1 and max at 1.