Funktion & Ableitungen
f(x) = e^{1 - x/2}·(2·x - 4)
f'(x) = e^{1 - x/2}·(4 - x)
f''(x) = e^{1 - x/2}·(x/2 - 3)
Verhalten im Unendlichen
lim (x --> -∞) f(x) = -∞
lim (x --> ∞) f(x) = 0
Nullstellen f(x) = 0
2·x - 4 = 0 --> x = 2
Extrempunkte f'(x) = 0
4 - x = 0 --> x = 4
f(4) = 4/e = 1.472 --> HP(4 | 1.472)
Wendepunkte f''(x) = 0
x/2 - 3 = 0 --> x = 6
f(6) = 8/e^2 = 1.083 --> WP(6 | 1.083)
Graph
~plot~ (2x - 4)*e^{1 - 0.5x};[[-1|9|-12|3]] ~plot~