Consider the function $z = x^{11}y + 33 x^{10} - 177147 y$. Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. The critical point with the smallest $x$-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

The critical point with the next smallest $x$-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

The critical point with the next smallest $x$-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

Your overall score for this problem is