The function $f(x,y)=x^4+y^4-4xy$ has three critical

points, $(0,0),(1,1)$ and $(-1,-1).At$ the point $(0,0),f(x,y)$

has $a.At$ the point $(1,1)$ and $at$ the point

$(-1,-1),f(x,y)$ has $a.in$ both cases.

Select your answer from the options listed. The first word $in$ each answer

choice fills $in$ the first answer blank, and the second word fills $in$ the

second answer blank.

local minimum; local minimum

local minimum; local maximum

local minimum; saddle point

local maximum; local minimum