Symmetrie zur y-Achse → f(x) = ax4 + bx2 + c
f(0) = 0 → c = 0 → f(x) = ax4 + bx2
f (2) = - 4 → 16a + 4b = - 4 → 4a + b = -1 #
f '(x) = 4ax3 + 2bx
f '(2) = 0 → 32a + 4b = 0 → b = - 8a
b in # → 4a - 8a = -1 → - 4a = -1 → a = 1/4 → b = - 2
f(x) = 1/4 · x4 - 2x2
Gruß Wolfgang