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Beliebt Funktionen >

extreme f(x)=(-5x^2+16x)/(2sqrt(4-x))

Lösung

extrempunkte

f (x) = \frac{- 5 x ^{2} + 16 x}{2 4 - x}

Lösung

Maximum (\frac{8 ( 6 - 6 )}{15}, \frac{32 ( 6 - 1 )}{15 3 + 2 6})

Schritte zur Lösung

f^{'} (x) = \frac{15 x ^{2} - 96 x + 128}{4 ( 4 - x ) 4 - x}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{8 2}{5 3} + \frac{16}{5},

Absteigend

: - \frac{8 2}{5 3} + \frac{16}{5} < x < 4

Stecke

x = \frac{8 ( 6 - 6 )}{15}

in

\frac{- 5 x ^{2} + 16 x}{2 4 - x} : \frac{32 ( 6 - 1 )}{15 3 + 2 6}

Maximum (\frac{8 ( 6 - 6 )}{15}, \frac{32 ( 6 - 1 )}{15 3 + 2 6})

Graph

Beliebte Beispiele

extreme f(x)=x^3-3x^2-3x-1

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

extreme f(x)=4x^2-8x+3

e x t re m e f (x) = 4 x^{2} - 8 x + 3

extreme f(x,y)=x^2+xy+1/2 y^2-5x+y

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

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

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

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

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