extreme f(x)=((x-4)^2)/(x+10)

Lösung

extrempunkte

f (x) = \frac{( x - 4 ) ^{2}}{x + 10}

Maximum (- 24, - 56), Minimum (4, 0)

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2} + 20 x - 96}{( x + 10 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 24,

Absteigend

: - 24 < x < - 10,

Absteigend

: - 10 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - 24

\frac{( x - 4 ) ^{2}}{x + 10} : - 56

Maximum (- 24, - 56)

Stecke

x = 4

\frac{( x - 4 ) ^{2}}{x + 10} : 0

Minimum (4, 0)

Maximum (- 24, - 56), Minimum (4, 0)

e x t re m e f (x) = 4 x - 1

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

e x t re m e f (x) = \frac{x}{x ^{2} + 100}

e x t re m e f (x) = 4 x - 9 x^{\frac{4}{9}}

e x t re m e f (x, y) = 3 x^{3} - 9 x + 9 x y^{2}