extreme f(x)=(1/12 x^3-1/2 x^2-12)

Lösung

extrempunkte

f (x) = (\frac{1}{12} x^{3} - \frac{1}{2} x^{2} - 12)

Maximum (0, - 12), Minimum (4, - \frac{44}{3})

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2}}{4} - x

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

\frac{1}{12} x^{3} - \frac{1}{2} x^{2} - 12 : - 12

Maximum (0, - 12)

Stecke

x = 4

\frac{1}{12} x^{3} - \frac{1}{2} x^{2} - 12 : - \frac{44}{3}

Minimum (4, - \frac{44}{3})

Maximum (0, - 12), Minimum (4, - \frac{44}{3})

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roo t s x θ

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