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

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.

Tom Mattson
Staff Emeritus
Gold Member
Yes. Just look at $f(x)=x^3$ in any interval containing $x=0$.

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

Tom Mattson
Staff Emeritus