Question

Find the critical points of the function f(x, y) = √(x²y² - 3).

A) (±√3, 0)
B) (0, ±√3)
C) (±√3, ±√3)
D) (0, 0)

Answer 1

To find the critical points of the function f(x, y) = √(x²y² - 3), we need to find the values of x and y that make the derivative of the function equal to zero.

Step-by-step explanation:

To find the critical points of the function f(x, y) = √(x²y² - 3), we need to find the values of x and y that make the derivative of the function equal to zero.

First, calculate the partial derivative of f with respect to x and y. The partial derivative with respect to x is: ∂f/∂x = 2xy² / √(x²y² - 3) and with respect to y is: ∂f/∂y = 2yx² / √(x²y² - 3).

To find the critical points, we need to set both partial derivatives equal to zero and solve for x and y. However, the given information provided in the question is not relevant and does not help in finding the critical points.