GR0568 Q26

Forum for the GRE subject test in mathematics.
aspirant
Posts: 7
Joined: Thu Nov 06, 2008 2:51 am

GR0568 Q26

Postby aspirant » Thu Nov 06, 2008 3:01 am

Hi, I can't figure out the answer to this question:

Let f(x,y) = x^2 - 2xy + y^3 for all real x and y. Which of the following is true?
(A) f has all of its relative extrema on the line x = y.
(B) f has all of its relative extrema on the parabola x = y2.
(C) f has a relative minimum at (0,0).
(D) f has an absolute minimum at (2/3, 2/3).
(E) f has an absolute minimum at (1, 1).

The answer is (A).

I chose (D) because point (0, 0) is a saddle point (and therefore not a relative extrema?) while point (2/3, 2/3) is indeed a minimum point. Can anyone please explain?

Much appreciated!!! :)

John

mathsubboy
Posts: 11
Joined: Sun Jul 20, 2008 12:11 pm

Postby mathsubboy » Thu Nov 06, 2008 7:13 am

note that f is not bounded from below!

Nameless
Posts: 128
Joined: Sun Aug 31, 2008 4:42 pm

Postby Nameless » Thu Nov 06, 2008 10:06 am

f has an absolute minimum at (2/3, 2/3).

try to read the question carefully :D stupid mistakes I always did :(

aspirant
Posts: 7
Joined: Thu Nov 06, 2008 2:51 am

Postby aspirant » Fri Nov 07, 2008 12:12 am

mathsubboy and Nameless, thanks!!! I am really careless! My test is tomorrow! I really can only hope for the best. I'm not a math major... these topics are really challenging!

So does this mean that a saddle point is a "relative extrema"? I guess the question implies this must be so!

sachem
Posts: 9
Joined: Wed Oct 29, 2008 8:01 pm

Postby sachem » Fri Nov 07, 2008 12:31 am

a saddle point is not a relative extrema. Only relative maxes and mins are.

thmsrhn
Posts: 17
Joined: Fri Mar 26, 2010 7:18 am

Re: GR0568 Q26

Postby thmsrhn » Sat Mar 27, 2010 8:29 am

what is a relative extrema and relative minimum?

origin415
Posts: 61
Joined: Fri Oct 23, 2009 11:42 pm

Re: GR0568 Q26

Postby origin415 » Sat Mar 27, 2010 11:33 am

thmsrhn wrote:what is a relative extrema and relative minimum?

relative min/max/extrema = local min/max/extrema if thats the term you are more familiar with. Its the largest or smallest value within some open neighborhood of the point, but not necessarily the largest/smallest on the entire domain.




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