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I'm trying to find the inflection points and concavity of the graph of

$$ x^4 - 50x^2 + 2 $$

The first derivative is

$$ 4x^3 - 100x $$

and the second derivative is

$$12x^2 - 100 $$

Trying to solve for x I keep getting

$$ \sqrt{(25/3)} $$

and the online assignment thing keeps telling me I'm getting it wrong. am I missing something?

Thank you!

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  • $\begingroup$ Note that $\sqrt {\frac{25}3}=\frac 53\sqrt3$ $\endgroup$ – Mark Bennet Apr 12 '14 at 17:46
  • $\begingroup$ The second derivative is a quadratic, so it should have 2 roots. Your answer is correct but forgot the negative of that square root. $\endgroup$ – Dylan Apr 12 '14 at 19:44
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You are nearly correct, just forgot to include $\pm$. There are two roots, opposite in sign.

You should also verify that the second derivative actually changes sign at each, otherwise they aren't inflection points.

Except for that, good work!

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