- #1

- 9

- 0

## Homework Statement

[tex] f(x) = x^{4} - 2x^{2} + 3[/tex]

Find the intervals of concavity and the inflection points.

## Homework Equations

[tex]f''(x) = 4(3x^{2}-1)[/tex]

## The Attempt at a Solution

[tex]f''(x)[/tex] is zero at [tex]\pm\frac{1}{\sqrt{3}}[/tex]

I've found the correct intervals of concavity, which are [tex](-\infty, -\frac{1}{\sqrt{3}}) \cup (\frac{1}{\sqrt{3}}, \infty)[/tex]

I would expect the inflection points to be [tex]\pm\frac{1}{\sqrt{3}}[/tex], which is partly correct, but the answer the book gives is [tex]\pm\frac{1}{\sqrt{3}}, \frac{22}{9}[/tex].

I can't see how [tex]\frac{22}{9}[/tex] could be an inflection point. It does not equal zero when plugged in to the second derivative.

Thanks