Find all stationary points of fx y xe-x y2 - 4y and

Question

Question: (a) Find all stationary points of f(x, y) = xe^-x (y² - 4y) and classify them by using the second-derivative test.

(b) Show that f has neither a global maximum nor a global minimum.

(c) Let S = {(x, y) : 0 ≤ x ≤ 5, 0 ≤ y ≤ 4 }. Prove that f has global maximum and minimum points in S and find them.

(d) Find the slope of the tangent to the level curve xe^-x (y² - 4y) = e - 4 at the point where x = 1 and y = 4_-e.