extreme-(8*x)/(x^2+1)

Lösung

extrempunkte

- \frac{8 \cdot x}{x ^{2} + 1}

Maximum (- 1, 4), Minimum (1, - 4)

Schritte zur Lösung

f^{'} (x) = - \frac{8 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

- \frac{8 \cdot x}{x ^{2} + 1} : 4

Maximum (- 1, 4)

Stecke

x = 1

- \frac{8 \cdot x}{x ^{2} + 1} : - 4

Minimum (1, - 4)

Maximum (- 1, 4), Minimum (1, - 4)

e x t re m e f (x) = x^{2} - y^{2} - 5 x - 4 y

e x t re m e f (x) = \frac{1}{x - 2}, 0 \leq x \leq 1

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

e x t re m e f (x) = - 2 x^{2} - 2 y^{2} + 20 x + 16 y + 4

e x t re m e \frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 2 x