(Solved): Suppose f(x,y)=xy(17x8y). f(x,y) has 4 critical points. List them in increasing lexograph ...

Suppose $f(x,y)=xy(1?7x?8y)$. $f(x,y)$ has 4 critical points. List them in increasing lexographic order. By that we mean that $(\mathrm{x},\mathrm{y})$ comes before $(\mathrm{z},\mathrm{w})$ if $x<z$ or if $x=z$ and $y<w$. Also, determine whether the critical point a local maximum, a local minimim, or a saddle point. First point (—, -). Classification: - local minimum - local maximum - saddle point - cannot be determined (local minimum, local maximum, saddle point, cannot be determined). Second point $(?,?)$.