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Beliebt Funktionen >

extreme f(x)=4x+9/x

Lösung

extrempunkte

f (x) = 4 x + \frac{9}{x}

Lösung

Maximum (- \frac{3}{2}, - 12), Minimum (\frac{3}{2}, 12)

Schritte zur Lösung

f^{'} (x) = 4 - \frac{9}{x ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{3}{2},

Absteigend

: - \frac{3}{2} < x < 0,

Absteigend

: 0 < x < \frac{3}{2},

Ansteigend

: \frac{3}{2} < x < \infty

Stecke

x = - \frac{3}{2}

in

4 x + \frac{9}{x} : - 12

Maximum (- \frac{3}{2}, - 12)

Stecke

x = \frac{3}{2}

in

4 x + \frac{9}{x} : 12

Minimum (\frac{3}{2}, 12)

Maximum (- \frac{3}{2}, - 12), Minimum (\frac{3}{2}, 12)

Graph

Beliebte Beispiele

extreme f(x)= 1/4 x^4-x^3-4x+2

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

extreme f(x)=x^3+2xy+y^2-5x

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e x t re m e f (x) = \frac{x ^{2} - 63}{x - 8}

extreme f(x)=x^2+y^4+2xy

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