extreme f(x)=(12x)/(9+x^2)

Lösung

extrempunkte

f (x) = \frac{12 x}{9 + x ^{2}}

Minimum (- 3, - 2), Maximum (3, 2)

Schritte zur Lösung

f^{'} (x) = \frac{12 ( 9 - x ^{2} )}{( 9 + x ^{2} ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 3

\frac{12 x}{9 + x ^{2}} : - 2

Minimum (- 3, - 2)

Stecke

x = 3

\frac{12 x}{9 + x ^{2}} : 2

Maximum (3, 2)

Minimum (- 3, - 2), Maximum (3, 2)

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

e x t re m e f (x) = \frac{4 x}{x ^{2} - 49}

e x t re m e f (x) = x^{3} - 6 x^{2} + 8, - 1 \leq x \leq 6

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

e x t re m e f (x, y) = x^{2} + x y + y^{2} - 6 y