Your having lunch at Taco Bell. You have your choice of a taco,burrito or Mexican pizza. You can choose between rice and beans.
Draw a tree diagram to show a sample space.
2 answers:
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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).