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

  • Thread starter frenkie
  • Start date
  • #1
37
0
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.
 

Answers and Replies

  • #2
Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
5,549
8
Yes. Just look at [itex]f(x)=x^3[/itex] in any interval containing [itex]x=0[/itex].
 
  • #3
1,056
0
Of course, and if you plot Y=X^3, you will see the change of slope at X=0.
 
  • #4
Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
5,549
8
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.
 

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

Replies
4
Views
1K
Replies
8
Views
766
  • Last Post
Replies
3
Views
4K
Replies
3
Views
2K
Replies
8
Views
1K
Replies
3
Views
12K
Replies
3
Views
2K
Top