During summer vacation, you charge $15 per hour for golf lessons and a registration fee of $45. If you make $120 one day, how ma
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First we note that the partial derivatives vanish simultaneously at one point:
so there is one critical point within the region
.
The Lagrangian is
and has partial derivatives
Set each partial derivative to 0 to find the possible critical points within the disk. Then we notice that
Since
, we have
And since
, or 
, we also have
So we have four possible additional critical points to consider:
It should be clear enough which of these correspond to the absolute extrema of
over .
so there is one critical point within the region
The Lagrangian is
and has partial derivatives
Set each partial derivative to 0 to find the possible critical points within the disk
Since
And since
So we have four possible additional critical points to consider:
It should be clear enough which of these correspond to the absolute extrema of