extreme f(x)=-(50x)/(x^2+25)

Lösung

extrempunkte

f (x) = - \frac{50 x}{x ^{2} + 25}

Maximum (- 5, 5), Minimum (5, - 5)

Schritte zur Lösung

f^{'} (x) = - \frac{50 ( - x ^{2} + 25 )}{( x ^{2} + 25 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 5,

Absteigend

: - 5 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = - 5

- \frac{50 x}{x ^{2} + 25} : 5

Maximum (- 5, 5)

Stecke

x = 5

- \frac{50 x}{x ^{2} + 25} : - 5

Minimum (5, - 5)

Maximum (- 5, 5), Minimum (5, - 5)

e x t re m e f (x, y) = - x^{4} + 2 y^{4} + 18 x^{2} - 36 y^{2} + 2

e x t re m e 5 cos (x)

e x t re m e f (x) = \frac{3}{5} (x^{2} - 1)^{\frac{2}{3}}

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

e x t re m e 81 - x^{2}, - 9 \leq x \leq 9