f(x) = e^(-x)·(x^2 + 2·x + k)
f'(x) = e^(-x)·(-x^2 - k + 2) = 0 --> k = 2 - x^2
Ortskurve der Extrempunkte
y = e^(-x)·(x^2 + 2·x + (2 - x^2)) = e^(-x)·(2·x + 2)
f''(x) = e^(-x)·(x^2 - 2·x + k - 2) = 0 --> k = -x^2 + 2·x + 2
Ortskurve der Wendepunkte
f(x) = e^(-x)·(x^2 + 2·x + (-x^2 + 2·x + 2)) = e^(-x)·(4·x + 2)