Determine whether the relation represents a function. State the domain and range of the relation.
1 answer:
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Answer:
B. the triangle in question is not a right triangle
Step-by-step explanation:
A 3-4-5 triangle is a right triangle, so this one, with its longer longest side, is an obtuse triangle. It is not a right triangle.
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3, 4, 5 is one of the first Pythagorean triples that you learn:
3² + 4² = 5²
These are the side lengths of the smallest right triangle with integer sides. It is worthwhile to remember. This triple is used not only in many math problems (such as this one), but also in real life when it is useful to lay out a right angle.
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