Final answer:
To find the critical points of the function f(x, y) = 16xye^(-x² - y²), take partial derivatives with respect to x and y, set them equal to zero, and solve the resulting system of equations.
Step-by-step explanation:
To find the critical points of the function f(x, y) = 16xye^(-x² - y²), we need to take partial derivatives with respect to x and y and set them equal to zero.
The partial derivative with respect to x is: fx(x, y) = 16(y - 2x²ye^(-x² - y²)).
The partial derivative with respect to y is: fy(x, y) = 16(x - 2y²xe^(-x² - y²)).
Setting both partial derivatives equal to zero, we can solve the resulting system of equations to find the critical points.
The critical points are the points (x, y) where both fx and fy are equal to zero.