Question

For f(x,y)=x³−y³ −2xy+6
Find all critical points for the function.

Answer 1

To find the critical points of the function f(x, y) = x³ - y³ - 2xy + 6, we need to find the values of x and y where the partial derivatives of the function are equal to zero.

Step-by-step explanation:

To find the critical points of the function f(x, y) = x³ - y³ - 2xy + 6, we need to find the values of x and y where the partial derivatives of the function are equal to zero. Let's start by finding the partial derivative with respect to x and setting it equal to zero:

∂f/∂x = 3x² - 2y = 0

Next, let's find the partial derivative with respect to y and set it equal to zero:

∂f/∂y = -3y² - 2x = 0

Solving these two equations simultaneously will give us the critical points of the function.