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Beliebt Funktionen >

extreme f(x)=(x^2-16)/(x-5)

Lösung

extrempunkte

f (x) = \frac{x ^{2} - 16}{x - 5}

Lösung

Maximum (2, 4), Minimum (8, 16)

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2} - 10 x + 16}{( x - 5 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < 2,

Absteigend

: 2 < x < 5,

Absteigend

: 5 < x < 8,

Ansteigend

: 8 < x < \infty

Stecke

x = 2

in

\frac{x ^{2} - 16}{x - 5} : 4

Maximum (2, 4)

Stecke

x = 8

in

\frac{x ^{2} - 16}{x - 5} : 16

Minimum (8, 16)

Maximum (2, 4), Minimum (8, 16)

Graph

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