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## Homework Statement

Find the critical point for z=(x^5)y+(xy^5)+xy

## Homework Equations

fx(x,y)=(5x^4)y+(y^5)+y=0

fy(x,y)=x^5+(5xy^4)+x=0

## The Attempt at a Solution

After finding fx and fy shown above, I attempt to find the critical points in one of the equations above, but the only number that works (that I can think of) is x=0 or y=0 and this doesn't seem correct to me after substituting it into the other equation. Am I doing something wrong?