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Can roots be at the same points as POI's?

  1. Mar 28, 2006 #1
    can roots be at the same points as POI's? because when I set my original equation to zero and I set my second derivative equation to zero i get the same answer? is it possible that roots can be same as the POI's.
     
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  3. Mar 28, 2006 #2

    Tom Mattson

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    Yes. Just look at [itex]f(x)=x^3[/itex] in any interval containing [itex]x=0[/itex].
     
  4. Mar 29, 2006 #3
    Of course, and if you plot Y=X^3, you will see the change of slope at X=0.
     
  5. Mar 29, 2006 #4

    Tom Mattson

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    Something else to ponder:

    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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