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Beliebt Funktionen >

extreme f(x)=3x^4-7ln(x)

Lösung

extrempunkte

f (x) = 3 x^{4} - 7 ln (x)

Lösung

Minimum (4 \frac{7}{12}, \frac{7}{4} - \frac{7}{4} ln (\frac{7}{12}))

Schritte zur Lösung

f^{'} (x) = 12 x^{3} - \frac{7}{x}

Intervalle finden:

Absteigend

: 0 < x < 4 \frac{7}{12},

Ansteigend

: 4 \frac{7}{12} < x < \infty

Stecke

x = 4 \frac{7}{12}

in

3 x^{4} - 7 ln (x) : \frac{7}{4} - \frac{7}{4} ln (\frac{7}{12})

Minimum (4 \frac{7}{12}, \frac{7}{4} - \frac{7}{4} ln (\frac{7}{12}))

Graph

Beliebte Beispiele

extreme f(x,y)=ln(9x^2+3y^2-4)

e x t re m e f (x, y) = ln (9 x^{2} + 3 y^{2} - 4)

extreme f(x)=3x^{2/3}-7

e x t re m e f (x) = 3 x^{\frac{2}{3}} - 7

extreme f(x,y)= 1/(x+y+3)

e x t re m e f (x, y) = \frac{1}{x + y + 3}

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

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

extreme (x^2+1)/(x^3-1)

e x t re m e \frac{x ^{2} + 1}{x ^{3} - 1}