I have the following problem to find critical points for and note whether I have any local minimas, saddle points, or local maximas.
I found the following partial derivatives:
and
Solving , I got: and
BUT, I can't figure out all of the points for:
I'm getting: ??
How do you get any critical points from that?
Any assistance will be appreciated!
Thank you in advance!
Jen
Ok.
So, when I do that for: :
I get when , and when
But....I don't understand how this works.
There seems to be an infinite set of answers for this equation which will = 0.
Does this mean there are no critical points for .
I'm sorry...I am unsure what you mean here. I thought I already computed the critical point for : (1,0) Am I wrong?to be safe, you can try to find the zeroes of as well, and plug those into . note that is quadratic in
Thanks Jhevon, for helping me with this.
~Jen
say y = 0, then for we have
. thus we have two critical points here: (0,0) and (2,0)
say x = 1, then for we have
. thus we have as another critical point.
now go on to classifying them
forget what i said there, i think i am just overkilling this. my point was that since , we have (by the quadratic formula)I'm sorry...I am unsure what you mean here. I thought I already computed the critical point for : (1,0) Am I wrong?
that will probably yield the same solutions we had anyway.