Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s).
62. f(x, y, z) = x2 + 2y2 + 3z2;
x + y + z =1, x − y + 2z = 2
To find: The extreme values of the function subject to the constraints by using Lagrange multipliers.
The function is subject to the constraints .
“The Lagrange multipliers defined as . This equation can be expressed as , , and , ”.
Let the function and .
The Lagrange multipliers is computed as follows.
Thus, the value of is .
The reuslt, can be expressed as follows.
From the equations (1), (2) and (3) and compute the values as follows
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