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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (\frac{- 3 - 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512}), Maximum (0, 0), Minimum (\frac{- 3 + 201}{8}, \frac{3 ( 67 201 - 1833 )}{512})

Schritte zur Lösung

f^{'} (x) = x (4 x^{2} + 3 x - 12)

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 3 - 201}{8},

Ansteigend

: \frac{- 3 - 201}{8} < x < 0,

Absteigend

: 0 < x < \frac{201 - 3}{8},

Ansteigend

: \frac{201 - 3}{8} < x < \infty

Stecke

x = \frac{- 3 - 201}{8}

in

x^{2} (x - 2) (x + 3) : - \frac{3 ( 1833 + 67 201 )}{512}

Minimum (\frac{- 3 - 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512})

Stecke

x = 0

in

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

Maximum (0, 0)

Stecke

x = \frac{- 3 + 201}{8}

in

x^{2} (x - 2) (x + 3) : \frac{3 ( 67 201 - 1833 )}{512}

Minimum (\frac{- 3 + 201}{8}, \frac{3 ( 67 201 - 1833 )}{512})

Minimum (\frac{- 3 - 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512}), Maximum (0, 0), Minimum (\frac{- 3 + 201}{8}, \frac{3 ( 67 201 - 1833 )}{512})

Graph

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