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Beliebt Funktionen >

extreme f(x)=5xsqrt(x-x^2)

Lösung

extrempunkte

f (x) = 5 x x - x^{2}

Lösung

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{15 3}{16}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = \frac{5 ( - 4 x ^{2} + 3 x )}{2 x - x ^{2}}

Intervalle finden:

Ansteigend

: 0 < x < \frac{3}{4},

Absteigend

: \frac{3}{4} < x < 1

Stecke

x = 0

in

5 x x - x^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{3}{4}

in

5 x x - x^{2} : \frac{15 3}{16}

Maximum (\frac{3}{4}, \frac{15 3}{16})

Stecke

x = 1

in

5 x x - x^{2} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{15 3}{16}), Minimum (1, 0)

Graph

Beliebte Beispiele

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

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

extreme f(x)=((x+4))/(x^2-3x-28)

e x t re m e f (x) = \frac{( x + 4 )}{x ^{2} - 3 x - 28}

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

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

extreme f(x,y)=2x^2y-2x^2-y^2

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

extreme f(x)=6x^2+7y^2

e x t re m e f (x) = 6 x^{2} + 7 y^{2}