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- Thread starter frenkie
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Tom Mattson

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Yes. Just look at [itex]f(x)=x^3[/itex] in any interval containing [itex]x=0[/itex].

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Of course, and if you plot Y=X^3, you will see the change of slope at X=0.

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Tom Mattson

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In your precalculus course you learned that you can shift a function vertically by adding a real number to it. That means that no matter what the y-coordinate of the POI of a function, you can always construct another function whose POI is a root, by doing an appropriate vertical shift.

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