A water well drilling rig has dug to a height of -15 feet in three hours. If the rig has been running constantly and is currentl
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Find the critical points of :
All three points lie within , and
takes on values of
Now check for extrema on the boundary of . Convert to polar coordinates:
Find the critical points of :
where is any integer. There are some redundant critical points, so we'll just consider
, which gives
which gives values of
So altogether, has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).