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

Lösung

extrempunkte

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

Sattel (0, 0), Maximum (\frac{3}{8}, \frac{27}{2048})

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 8 x^{3}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{3}{8},

Absteigend

: \frac{3}{8} < x < \infty

Stecke

x = 0

x^{3} (1 - 2 x) : 0

Sattel (0, 0)

Stecke

x = \frac{3}{8}

x^{3} (1 - 2 x) : \frac{27}{2048}

Maximum (\frac{3}{8}, \frac{27}{2048})

Sattel (0, 0), Maximum (\frac{3}{8}, \frac{27}{2048})

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