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Beliebt Funktionen >

extreme f(x)=80x^{1/4}-x^{5/4}

Lösung

extrempunkte

f (x) = 80 x^{\frac{1}{4}} - x^{\frac{5}{4}}

Lösung

Minimum (0, 0), Maximum (16, 128)

Schritte zur Lösung

f^{'} (x) = \frac{80 - 5 x}{4 x ^{\frac{3}{4}}}

Intervalle finden:

Ansteigend

: 0 < x < 16,

Absteigend

: 16 < x < \infty

Stecke

x = 0

in

80 x^{\frac{1}{4}} - x^{\frac{5}{4}} : 0

Minimum (0, 0)

Stecke

x = 16

in

80 x^{\frac{1}{4}} - x^{\frac{5}{4}} : 128

Maximum (16, 128)

Minimum (0, 0), Maximum (16, 128)

Graph

Beliebte Beispiele

extreme f(x)=120t-16t^2

e x t re m e f (x) = 120 t - 16 t^{2}

extreme x^2-y^2+1

e x t re m e x^{2} - y^{2} + 1

extreme f(x,y)=9x^2-2x^3+3y^2+6xy

e x t re m e f (x, y) = 9 x^{2} - 2 x^{3} + 3 y^{2} + 6 x y

extreme f(x)=395x^2-2370x^3,0<= x<= 0.16

e x t re m e f (x) = 395 x^{2} - 2370 x^{3}, 0 \leq x \leq 0.16

extreme C(t)= t/(4t^2+11)

e x t re m e C (t) = \frac{t}{4 t ^{2} + 11}