GR0568 Q26

[aspirant]

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]

note that f is not bounded from below!

[Nameless]

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

try to read the question carefully stupid mistakes I always did

[aspirant]

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]

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

[thmsrhn]

what is a relative extrema and relative minimum?

[origin415]

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.