1
$\begingroup$

How do i determine maximum or minimum at this point of function

$$ f(x,y)=(x-y)^{4} + (y-1)^{4}$$

I am getting doubtful case at point (1,1). How do i furthure investigate whether it is point of minima or maxima

Thanks

$\endgroup$
7
$\begingroup$

Hint:

Notice that you add $2$ non - negative terms! Thus, $f(x,y) \ge 0,$ for all $x,y \in \mathbb R$. For which $x,y$ does it hold $f(x,y) = 0$?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.