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Lagrange multipliers:
(if 
)
(if )
(if 
)
In the first octant, we assume
, so we can ignore the caveats above. Now,
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
.
We also need to check the boundary of the region, i.e. the intersection of
with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force 
, so the point we found is the only extremum.
In the first octant, we assume
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
We also need to check the boundary of the region, i.e. the intersection of
The length of the radius of circle o is 18 cm.
<h2></h2><h2>Given that</h2>
Circle o has a circumference of 36π cm.
<h3>We have to determine</h3>
What is the length of the radius, r?
<h3>According to the question</h3>Circle o has a circumference of 36π cm.
The length of the radius of the circle is determined by the following formula;
Substitute all the values in the formula;
Hence, the length of the radius of circle o is 18 cm.
To know more about Circumference click the link given below.