Final answer:
The global maximum of the function f(x, y) = x+y on the given domain is 8, and the global minimum is 0.
Step-by-step explanation:
To determine the global extreme values of the function f(x, y) = x+y given the constraints 0 ≤ x ≤ 4 and 0 ≤ y ≤ 4, we do not need calculus since the function is linear and the constraints define a rectangle in the first quadrant of the xy-plane.
The global maximum occurs at the point where both x and y have their maximum values within the given constraints, which is at (4, 4). Hence, f(4, 4) = 4+4 = 8.
The global minimum occurs at the point where both x and y have their minimum values, which is at (0, 0). Hence, f(0, 0) = 0+0 = 0.
To determine the global extreme values of the function f(x, y) = x+y, we need to consider the given constraints 0 ≤ x ≤ 4 and 0 ≤ y ≤ 4. The function represents a plane with a slope of 1, which means it increases uniformly as both x and y increase.
The global maximum value occurs at the point (4, 4), where x and y reach their maximum values. So the global maximum is 4 + 4 = 8.
The global minimum value occurs at the point (0, 0), where x and y reach their minimum values. So the global minimum is 0 + 0 = 0.