Solve the problem. Round the point estimate to the nearest thousandth. Find the point estimate of the proportion of people who w
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You're looking for the extreme values of subject to the constraint
.
The target function has partial derivatives (set equal to 0)
so there is only one critical point at . But this point does not fall in the region
. There are no extreme values in the region of interest, so we check the boundary.
Parameterize the boundary of by
with . Then
can be considered a function of
alone:
has critical points where
:
but for all
, so this case yields nothing important.
At these critical points, we have temperatures of
so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.