(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

Find the intervals of concavity and the inflection points.

2. Relevant equations

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

3. 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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Inflection point confusion

**Physics Forums | Science Articles, Homework Help, Discussion**