Answer :
Final answer:
Option (a), The method to find the extrema of the function given a constraint is the Lagrange Multipliers. It involves setting up a Lagrange function and finding its critical points by solving the system of equations obtained from the partial derivatives set to zero.
Explanation:
The method used to find the extrema of the function f(x,y)=83-x²-y² under the constraint xy-2=0 is a) Lagrange Multipliers. This technique allows us to find the local maxima and minima of a function subject to equality constraints. In this case, the Lagrange function would be L(x, y, λ) = 83 - x² - y² + λ(xy - 2), where λ is the Lagrange multiplier.
The extrema are found by calculating the partial derivatives of L with respect to x, y, and λ, and setting them equal to zero. The solutions to these equations should give the values of x, y, and λ that satisfy both the original function and the constraint.
