f(x) = - 0.5·x^4 + 2·x^2 + 4
f'(x) = 4·x - 2·x^3
f''(x) = 4 - 6·x^2
Nullstellen f(x) = 0
- 0.5·x^4 + 2·x^2 + 4 = 0
- 0.5·z^2 + 2·z + 4 = 0
z = 2 - 2·√3 ∨ z = 2·√3 + 2
Resubstitution
x = - √(√12 + 2) ∨ x = √(√12 + 2)
Extrempunkte f'(x) = 0
4·x - 2·x^3 = 0
x = - √2 ∨ x = √2 ∨ x = 0
f(0) = 4 --> Tiefpunkt
f(± √2) = 6 --> Hochpunkte
Wendepunkte f''(x) = 0
4 - 6·x^2 = 0
x = - √6/3 ∨ x = √6/3
f(√6/3) = 46/9
