extreme f(x)=(2(x+7)^2)/(x+10)

Lösung

extrempunkte

f (x) = \frac{2 ( x + 7 ) ^{2}}{x + 10}

Maximum (- 13, - 24), Minimum (- 7, 0)

Schritte zur Lösung

f^{'} (x) = \frac{2 ( x ^{2} + 20 x + 91 )}{( x + 10 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 13,

Absteigend

: - 13 < x < - 10,

Absteigend

: - 10 < x < - 7,

Ansteigend

: - 7 < x < \infty

Stecke

x = - 13

\frac{2 ( x + 7 ) ^{2}}{x + 10} : - 24

Maximum (- 13, - 24)

Stecke

x = - 7

\frac{2 ( x + 7 ) ^{2}}{x + 10} : 0

Minimum (- 7, 0)

Maximum (- 13, - 24), Minimum (- 7, 0)

e x t re m e \frac{2 x ^{2} - 5 x + 5}{x - 2}

e x t re m e f (x) = 2 x^{2} - 12 x + 20

e x t re m e f (x) = 4 sin^{2} (x), 0 \leq x \leq π

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

e x t re m e f (x, y) = 4 x^{2} + \frac{1}{4} y^{3} - 2 x y