PG entrance exam IIT JAM 2025 Mock Test Mathematical Science Analysis Functions of Several Variables
Consider the functions \(f(x, y) = x^2 + y^2 \) and g(x, y) = x + y defined on\( \mathbb{R}^2 \). Suppose we are restricted to the constraint g(x, y) = 1 .
Which of the following statements is true?
1
The function f has no global extreme value subject to the constraint g(x, y) = 1 .
2
The function f has global extreme values at the points where \(x = \pm 1, y = 0 \quad or \quad x = 0, y = \pm 1 \).
3
The function g has no global extreme value subject to the constraint f(x, y) = 1 .
4
The function g has a global extreme value at (0, 1) subject to the constraint f(x, y) = 1 .