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Answer:
Maximum value:
Minimum value:
Step-by-step explanation:
Let , the restriction function.The Lagrange Multiplier problem states that an extreme (x1, ..., xn) of f with the constraint g(x) = 9 has to follow the following rule:
for a constant .
Note that the partial derivate of f respect to any variable is 1, and the partial derivate of g respect xi is 2xi, this means that
Thus,
Where c is a constant that doesnt depend on i. In other words, there exists c such that (x1, x2, ..., xn) = (c,c, ..., c). Now, since g(x1, ..., xn) = 9, we have that n * c² = 9, or
When c is positive, f reaches a maximum, which is
On the other hand, when c is negative, f reaches a minimum,