Question

Question #a4fd4

Answer 1

Extrema are found by differentiating f(x) and setting f ' equal to zero. This equation yields the critical points/potential local extrema.

Explanation:

Differentiating 8 / (x^2 +1) by rewriting it as
8 (x^2 +1)^-1 so the Power Rule and Chain Rule can be applied.
This results in
f '(x) = (8) -1 (x^2 +1)^-2 (2x) = -16x (x^2 +1)^-2
Setting this = 0 gives a solution of x = 0

This is a local maximum on the y axis at y=8.

I graphed this to double check and it looks right
But I do not understand why the 2nd Derivative is not negative
which is what one expects for a local maximum.
Maybe others can see the contradiction and explain this.