extreme (5x)/(x^2+9)

Lösung

extrempunkte

\frac{5 x}{x ^{2} + 9}

Minimum (- 3, - \frac{5}{6}), Maximum (3, \frac{5}{6})

Schritte zur Lösung

f^{'} (x) = \frac{5 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 3

\frac{5 x}{x ^{2} + 9} : - \frac{5}{6}

Minimum (- 3, - \frac{5}{6})

Stecke

x = 3

\frac{5 x}{x ^{2} + 9} : \frac{5}{6}

Maximum (3, \frac{5}{6})

Minimum (- 3, - \frac{5}{6}), Maximum (3, \frac{5}{6})

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

e x t re m e 3 x + y

e x t re m e f (x) = \frac{e ^{x}}{( 3 + e ^{x} )}

e x t re m e f (x) = - x^{2} + 190

e x t re m e f (x) = 28 x - \frac{x ^{2}}{105}