This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x1, x2, ..., xn) = x1 + x2 + ... + xn; x12 + x22 + ... + xn2 = 9

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,

from the sentence, "tomorrow morning, akiko will arrive an hour late" depicts a third person perspective because it doesn't use any pronoun to replace akiko, the subject of the sentence, and it is in singular form since akiko is only one person.

804.75

step-by-step explanation: