extreme f(x)=(x^2-4)/(x-4)

Lösung

extrempunkte

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

Maximum (2 (2 - 3), \frac{4 ( 2 3 - 3 )}{3}), Minimum (2 (2 + 3), \frac{4 ( 3 + 2 3 )}{3})

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2} - 8 x + 4}{( x - 4 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < 2 (2 - 3),

Absteigend

: 2 (2 - 3) < x < 4,

Absteigend

: 4 < x < 2 (2 + 3),

Ansteigend

: 2 (2 + 3) < x < \infty

Stecke

x = 2 (2 - 3)

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

Maximum (2 (2 - 3), \frac{4 ( 2 3 - 3 )}{3})

Stecke

x = 2 (2 + 3)

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

Minimum (2 (2 + 3), \frac{4 ( 3 + 2 3 )}{3})

Maximum (2 (2 - 3), \frac{4 ( 2 3 - 3 )}{3}), Minimum (2 (2 + 3), \frac{4 ( 3 + 2 3 )}{3})

e x t re m e f (x) = 3 x^{4} + 3

e x t re m e f (x) = x ln (\frac{x}{2})

e x t re m e f (x) = \frac{1}{2} (3 x - 1)

e x t re m e f (x) = - \frac{2 x}{5 x ^{2} + 8}

e x t re m e f (x) = 2 x^{3} + 6 x - 90 x + 5, - 5 < x < 4