Consider the function $z = x^7y + 49x^6 - 823543y$. 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)