Using Lagrange Multipliers In Exercises 1-12, use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. See Example 1.
Minimize
Constraint:
To calculate: The minimum value of the function
Given Information:
The provided function is
Formula used:
Method of Lagrange multipliers,
If the function
Steps to determine the minimum or maximum of the function
1. Solve the system of equations,
2. Determine the value of the function
The largest value gives the maximum value of function
Calculation:
Consider the function,
The provided constraint is
So,
Now, the new function
Differentiate above equation with respect to
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