extreme (x^2+2)/(x-3)

Lösung

extrempunkte

\frac{x ^{2} + 2}{x - 3}

Maximum (3 - 11, - \frac{22 - 6 11}{11}), Minimum (3 + 11, \frac{22 + 6 11}{11})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 3 - 11,

Absteigend

: 3 - 11 < x < 3,

Absteigend

: 3 < x < 3 + 11,

Ansteigend

: 3 + 11 < x < \infty

Stecke

x = 3 - 11

\frac{x ^{2} + 2}{x - 3} : - \frac{22 - 6 11}{11}

Maximum (3 - 11, - \frac{22 - 6 11}{11})

Stecke

x = 3 + 11

\frac{x ^{2} + 2}{x - 3} : \frac{22 + 6 11}{11}

Minimum (3 + 11, \frac{22 + 6 11}{11})

Maximum (3 - 11, - \frac{22 - 6 11}{11}), Minimum (3 + 11, \frac{22 + 6 11}{11})

e x t re m e f (x) = 5 + \frac{48}{x} + 3 x^{2}

e x t re m e E (x, y) = 15 x y - 22 x y

e x t re m e f (x) = 4 (x - 4)^{\frac{2}{3}}

e x t re m e f (x) = 2 x^{2} + 16 x - 5

e x t re m e f (x) = x (x - 1)^{5}