Find critical points, intervals for increase and decrease, relative maxima and minima, concave up and down, points of inflection, horizontal and vertical asymptotes, global max and min, draw graph with all those features for function: f(x)=x/x^2+1

Question

anonymous · Answer

I found the f'(x)=1-x^2/(x^2+1)^2

                 f''(x)=2x^3-6x/(x^2+1)^3

anonymous · Answer

-Critical points are found when you set the derivative of the equation to zero.
-You can determine if that point is a max or min by plugging into the second derivative, if it is positive, then it is a min, if it is negative, then it is a max.
-The inflection points are found by taking the second derivative and setting it equal to zero.
-x-int are found by plugging zero in for y in the original equation and solving.
-y-int are found by plugging zero in for x in the original equation and solving.

anonymous · Answer

thanks you!!

anonymous · Answer

No problem

anonymous · Answer

so to determine the min or max u plug the critical  points into the second derivative>

anonymous · Answer

what about where the function is decreasing and increasing