extreme x/(x^2+100)

Lösung

extrempunkte

\frac{x}{x ^{2} + 100}

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} + 100}{( x ^{2} + 100 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 10,

Ansteigend

: - 10 < x < 10,

Absteigend

: 10 < x < \infty

Stecke

x = - 10

\frac{x}{x ^{2} + 100} : - \frac{1}{20}

Minimum (- 10, - \frac{1}{20})

Stecke

x = 10

\frac{x}{x ^{2} + 100} : \frac{1}{20}

Maximum (10, \frac{1}{20})

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

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

e x t re m e f (x) = 2 x + sin (4 x)

e x t re m e f (x) = - 2 x^{2} + 12 x - 10

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

e x t re m e f (x) = \frac{x + 1}{x ^{2} - 4 x - 5}