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

Lösung

extrempunkte

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

Minimum (- 5, - \frac{1}{10}), Maximum (5, \frac{1}{10})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < 5,

Absteigend

: 5 < x < \infty

Stecke

x = - 5

\frac{x}{25 + x ^{2}} : - \frac{1}{10}

Minimum (- 5, - \frac{1}{10})

Stecke

x = 5

\frac{x}{25 + x ^{2}} : \frac{1}{10}

Maximum (5, \frac{1}{10})

Minimum (- 5, - \frac{1}{10}), Maximum (5, \frac{1}{10})

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

e x t re m e f (x) = x^{2} - 4 x + 9

e x t re m e 1 - e^{- 0.5 x}

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

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