Find the slope of the tangent to the level curve

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Reference no: EM131567281

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.

Reference no: EM131567281

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