Science:Math Exam Resources/Courses/MATH100 C/December 2024/Question 10 (b)/Statement

Consider the function

$f (x, y) = x y$

on the domain $x^{2} + y^{2} \leq 1 .$

Find all points of interest on the boundary of the domain using the Lagrange Multiplier technique. Give your answer as ordered pairs (that is, include both the $x -$ and $y -$ value of each point).

This question tests your facility with Lagrange multipliers. Any other techniques will receive no credit.