Concavity and Points of Inflection

Question

For the function $$f(x)=\frac{x}{x^2+1}$$, which of the following statements is true regarding its points of inflection as determined by the second derivative?

Accepted Answer

The function has points of inflection at $$x = -\sqrt{3}$$, $$x = 0$$, and $$x = \sqrt{3}$$, where the concavity changes sign.

Answer

The function has points of inflection at x = 0 and x = 2, which is a miscalculation based on the second derivative.

Answer

The function has a single point of inflection at x = 0, with no inflection points at $$x = \pm\sqrt{3}$$.

Answer

There are no points of inflection because the second derivative is always positive.

Concavity and Points of Inflection

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