I am struggling with this question which appears in every adv. calculus exam paper I practise and would love some help or advice on how to even approach it! I have no trouble getting the extreme points and determining whether they are local minimum, local maximum or saddle points, but proving that a function with 2 variables does not achieve a global max or min is proving very difficult. Here is an example of a question:(adsbygoogle = window.adsbygoogle || []).push({});

1.Let f(x,y)=y^2+2xy+x^3-x. Find the critical points of f and classify each of them as a local maximum, a local minimum or a saddle point.

(The answers I have come up with for this part are : (-1/3, 1/3) is a saddle point and (1,-1) is a local minimum.

2.Consider the values of f on the x- axis, or otherwise, to show that f has neither a global maximum nor a global minimum.

I don't know what to do here, especially since I am not given an interval...

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# Trouble proving a function with 2 variables does not have a global max or global min

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