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Beliebt Funktionen >

extreme 3/((x-1)(x^2-4))

Lösung

extrempunkte

\frac{3}{( x - 1 ) ( x ^{2} - 4 )}

Lösung

Minimum (\frac{1 - 13}{3}, - \frac{35 - 13 13}{24}), Maximum (\frac{1 + 13}{3}, - \frac{35 + 13 13}{24})

Schritte zur Lösung

f^{'} (x) = - \frac{3 ( 3 x ^{2} - 2 x - 4 )}{( x - 1 ) ^{2} ( x ^{2} - 4 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < \frac{1 - 13}{3},

Ansteigend

: \frac{1 - 13}{3} < x < 1,

Ansteigend

: 1 < x < \frac{1 + 13}{3},

Absteigend

: \frac{1 + 13}{3} < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = \frac{1 - 13}{3}

in

\frac{3}{( x - 1 ) ( x ^{2} - 4 )} : - \frac{35 - 13 13}{24}

Minimum (\frac{1 - 13}{3}, - \frac{35 - 13 13}{24})

Stecke

x = \frac{1 + 13}{3}

in

\frac{3}{( x - 1 ) ( x ^{2} - 4 )} : - \frac{35 + 13 13}{24}

Maximum (\frac{1 + 13}{3}, - \frac{35 + 13 13}{24})

Minimum (\frac{1 - 13}{3}, - \frac{35 - 13 13}{24}), Maximum (\frac{1 + 13}{3}, - \frac{35 + 13 13}{24})

Graph

Beliebte Beispiele

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