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Beliebt Funktionen >

extreme f(x)=-2/5 x^{5/2}+32x^{1/2}

Lösung

extrempunkte

f (x) = - \frac{2}{5} x^{\frac{5}{2}} + 32 x^{\frac{1}{2}}

Lösung

Minimum (0, 0), Maximum (4, \frac{256}{5})

Schritte zur Lösung

f^{'} (x) = \frac{16 - x ^{2}}{x ^{\frac{1}{2}}}

Intervalle finden:

Ansteigend

: 0 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = 0

in

- \frac{2}{5} x^{\frac{5}{2}} + 32 x^{\frac{1}{2}} : 0

Minimum (0, 0)

Stecke

x = 4

in

- \frac{2}{5} x^{\frac{5}{2}} + 32 x^{\frac{1}{2}} : \frac{256}{5}

Maximum (4, \frac{256}{5})

Minimum (0, 0), Maximum (4, \frac{256}{5})

Graph

Beliebte Beispiele

extreme f(x)=((-2x)/(x^2+7))

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

extreme f(x,y)=(x^2-8x)(y^2-3y)

e x t re m e f (x, y) = (x^{2} - 8 x) (y^{2} - 3 y)

extreme F(x)=(5x^2)/(x^2-16)

e x t re m e F (x) = \frac{5 x ^{2}}{x ^{2} - 16}

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

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

extreme 16(-1/(x^2)-2/(x^3))

e x t re m e 16 (- \frac{1}{x ^{2}} - \frac{2}{x ^{3}})