extreme f(x)=(16-2x)(12-2x)x

Lösung

extrempunkte

f (x) = (16 - 2 x) (12 - 2 x) x

Maximum (\frac{2 ( 7 - 13 )}{3}, \frac{2240 + 832 13}{27}), Minimum (\frac{2 ( 7 + 13 )}{3}, \frac{2240 - 832 13}{27})

Schritte zur Lösung

f^{'} (x) = 4 (3 x^{2} - 28 x + 48)

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 2 13 + 14}{3},

Absteigend

: \frac{- 2 13 + 14}{3} < x < \frac{2 13 + 14}{3},

Ansteigend

: \frac{2 13 + 14}{3} < x < \infty

Stecke

x = \frac{2 ( 7 - 13 )}{3}

(16 - 2 x) (12 - 2 x) x : \frac{2240 + 832 13}{27}

Maximum (\frac{2 ( 7 - 13 )}{3}, \frac{2240 + 832 13}{27})

Stecke

x = \frac{2 ( 7 + 13 )}{3}

(16 - 2 x) (12 - 2 x) x : \frac{2240 - 832 13}{27}

Minimum (\frac{2 ( 7 + 13 )}{3}, \frac{2240 - 832 13}{27})

Maximum (\frac{2 ( 7 - 13 )}{3}, \frac{2240 + 832 13}{27}), Minimum (\frac{2 ( 7 + 13 )}{3}, \frac{2240 - 832 13}{27})

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e x t re m e 280

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