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

Lösung

extrempunkte

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

Maximum (2, 0), Minimum (\frac{8}{3}, - \frac{4}{27})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 2,

Absteigend

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

Ansteigend

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

Stecke

x = 2

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

Maximum (2, 0)

Stecke

x = \frac{8}{3}

(x - 3) (x - 2)^{2} : - \frac{4}{27}

Minimum (\frac{8}{3}, - \frac{4}{27})

Maximum (2, 0), Minimum (\frac{8}{3}, - \frac{4}{27})

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e x t re m e 0.01 x^{3} - 0.45 x^{2} + 2 x + 300