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6
a) `F(x) = (x-3)^5 + C`

n) `F(x) = - 2* (-cos(-t)) + C = 2*cos(-t) + C`

p) `F(x) = sqrt 2 * (-2)* sin(-1/2 t) + C`




13
`f(x) = 1/18(x^3-9x^2+108)`

a) Extrempunkte: `f'(x) = 1/18(3 x^2 - 18x) = 1/6 x^2 - x = x*(1/6 x - 1)`

`f'(x) = 0 => x_1 = 0; x_2 = 6;`

VZT`x lt 0``x=0``0 lt x lt 6``x=6``6 lt x`
`f'(x)`+0-0+
`G_f`↗HOP↘TIP↗
Koordinaten der Punkte:

`f(0) = 6 => HOP(0;6); f(6) = 12-18+6 = 0 => TIP(6;0)` b) `f''(x) = 1/3 x - 1`

`f''(x) = 0 => x = 3` (Wendestelle)

`f(3) = 3/2 - 9/2 + 6 = 3 => WEP(3;3)`

Wendetangente, Steigung `m_W`:

`f'(3) = 9/6 - 3 = -1.5`

Wendetangente, y-Achsenabschnitt `t_W`:

`3 = -1.5*3 + t_W => t_W = 7.5`

`W(x) = -1.5 x + 7.5`