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The function is as follows

$-2x^3+6x-4$
enter image description here

The sign diagram for that in the book is as follows: enter image description here

As seen on the pic and graph it is only positive before -2, NOT after 1. Or did I miss something?

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Which tool do you use to plot this inequality? – Quixotic Oct 16 '11 at 11:41
wolframalpha :) – Algific Oct 16 '11 at 11:42
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You are correct that it is not positive for $x\gt1$. – Gerry Myerson Oct 16 '11 at 11:44
I was unsure because the sign diagram for the derivative would be sort the inverse of this and that had a nice symmetry to it. – Algific Oct 16 '11 at 11:45
You can know there's something wrong with the book's diagram even without plotting, because a polynomial of odd degree will always have different signs for $x\to\infty$ and $x\to-\infty$. – Henning Makholm Oct 16 '11 at 16:09

1 Answer

up vote 2 down vote accepted

Yes, the book seems to be wrong. The most likely explanation is that they found roots at $x = -2$ and $x = 1$, but didn't realize that the second one doesn't actually change the sign of the function.

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