a)
h(x) = - x^3 + 10·x^2 - 11·x - 22
h'(x) = - 3·x^2 + 20·x - 11
h''(x) = 20 - 6·x
b)
man löst die quadratische Gleichung h'(xm) = 0
c)
h'(6.1) = - 3·(6.1)^2 + 20·(6.1) - 11 = -0.63 --> Da ist kein Hochpunkt
- 3·x^2 + 20·x - 11 = 0 --> x = √67/3 + 10/3 = 6.062
h''(6.062) = 20 - 6·6.062 < 0 --> Hochpunkt
d)
h''(x) = 20 - 6·x = 0 --> x = 10/3
h'(10/3) = - 3·(10/3)^2 + 20·(10/3) - 11 = 67/3 = 22.33
e)
H(x) = - 1/4·x^4 + 10/3·x^3 - 11/2·x^2 - 22·x + c