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Beliebt Funktionen >

extreme f(x)=(x^2+12)/(x-3)

Lösung

extrempunkte

f (x) = \frac{x ^{2} + 12}{x - 3}

Lösung

Maximum (3 - 21, - \frac{14 3 - 6 7}{7}), Minimum (3 + 21, \frac{14 3 + 6 7}{7})

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2} - 6 x - 12}{( x - 3 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < 3 - 21,

Absteigend

: 3 - 21 < x < 3,

Absteigend

: 3 < x < 3 + 21,

Ansteigend

: 3 + 21 < x < \infty

Stecke

x = 3 - 21

in

\frac{x ^{2} + 12}{x - 3} : - \frac{14 3 - 6 7}{7}

Maximum (3 - 21, - \frac{14 3 - 6 7}{7})

Stecke

x = 3 + 21

in

\frac{x ^{2} + 12}{x - 3} : \frac{14 3 + 6 7}{7}

Minimum (3 + 21, \frac{14 3 + 6 7}{7})

Maximum (3 - 21, - \frac{14 3 - 6 7}{7}), Minimum (3 + 21, \frac{14 3 + 6 7}{7})

Graph

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