extreme f(x)=((x^2-11x+82))/(x-9)

Lösung

extrempunkte

f (x) = \frac{( x ^{2} - 11 x + 82 )}{x - 9}

Maximum (1, - 9), Minimum (17, 23)

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2} - 18 x + 17}{( x - 9 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < 1,

Absteigend

: 1 < x < 9,

Absteigend

: 9 < x < 17,

Ansteigend

: 17 < x < \infty

Stecke

x = 1

\frac{x ^{2} - 11 x + 82}{x - 9} : - 9

Maximum (1, - 9)

Stecke

x = 17

\frac{x ^{2} - 11 x + 82}{x - 9} : 23

Minimum (17, 23)

Maximum (1, - 9), Minimum (17, 23)