extreme f(x)=x(40-2x)^2

Lösung

extrempunkte

f (x) = x (40 - 2 x)^{2}

Maximum (\frac{20}{3}, \frac{128000}{27}), Minimum (20, 0)

Schritte zur Lösung

f^{'} (x) = 4 (x - 20) (3 x - 20)

Intervalle finden:

Ansteigend

: - \infty < x < \frac{20}{3},

Absteigend

: \frac{20}{3} < x < 20,

Ansteigend

: 20 < x < \infty

Stecke

x = \frac{20}{3}

x (40 - 2 x)^{2} : \frac{128000}{27}

Maximum (\frac{20}{3}, \frac{128000}{27})

Stecke

x = 20

x (40 - 2 x)^{2} : 0

Minimum (20, 0)

Maximum (\frac{20}{3}, \frac{128000}{27}), Minimum (20, 0)

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