e(t) = - 1/400·t^2·(t - 48) = 0.12·t^2 - 0.0025·t^3
e'(t) = 0.24·t - 0.0075·t^2
e''(t) = 0.24 - 0.015·t
Nullstellen e(t) = 0
0.12·t^2 - 0.0025·t^3 = 0 --> t = 0 ∨ t = 48
Extremstellen e'(t) = 0
0.24·t - 0.0075·t^2 = 0 --> t = 0 ∨ t = 32
Wendestellen e''(t) = 0
0.24 - 0.015·t = 0 --> t = 16
Skizze
~plot~ 0.12x^2-0.0025x^3;[[-5|55|-5|45]] ~plot~