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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (0, 5), Minimum (2500, 50 0^{5} - 250 0^{4} + 5)

Schritte zur Lösung

f^{'} (x) = \frac{x ^{4}}{625} - 4 x^{3}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 2500,

Ansteigend

: 2500 < x < \infty

Stecke

x = 0

in

(\frac{x}{5})^{5} - (\frac{4 x}{4})^{4} + 5 : 5

Maximum (0, 5)

Stecke

x = 2500

in

(\frac{x}{5})^{5} - (\frac{4 x}{4})^{4} + 5 : 50 0^{5} - 250 0^{4} + 5

Minimum (2500, 50 0^{5} - 250 0^{4} + 5)

Maximum (0, 5), Minimum (2500, 50 0^{5} - 250 0^{4} + 5)

Graph

Beliebte Beispiele

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

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

extreme f(x)=x^4-2x^3-11x^2+12x+36

e x t re m e f (x) = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36

extreme y=9x^3-7

e x t re m e y = 9 x^{3} - 7

extreme x^3-12x^2+45x+8

e x t re m e x^{3} - 12 x^{2} + 45 x + 8

extreme |x^4-4x^2-2|,-2<= x<= 2

e x t re m e x^{4} - 4 x^{2} - 2, - 2 \leq x \leq 2