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Beliebt Funktionen >

extreme f(x)=x(25-2x)(48/2-x)

Lösung

extrempunkte

f (x) = x (25 - 2 x) (\frac{48}{2} - x)

Lösung

Maximum (\frac{73 - 1729}{6}, \frac{5183 + 1729 1729}{54}), Minimum (\frac{73 + 1729}{6}, \frac{5183 - 1729 1729}{54})

Schritte zur Lösung

f^{'} (x) = 2 (3 x^{2} - 73 x + 300)

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 1729 + 73}{6},

Absteigend

: \frac{- 1729 + 73}{6} < x < \frac{1729 + 73}{6},

Ansteigend

: \frac{1729 + 73}{6} < x < \infty

Stecke

x = \frac{73 - 1729}{6}

in

x (25 - 2 x) (\frac{48}{2} - x) : \frac{5183 + 1729 1729}{54}

Maximum (\frac{73 - 1729}{6}, \frac{5183 + 1729 1729}{54})

Stecke

x = \frac{73 + 1729}{6}

in

x (25 - 2 x) (\frac{48}{2} - x) : \frac{5183 - 1729 1729}{54}

Minimum (\frac{73 + 1729}{6}, \frac{5183 - 1729 1729}{54})

Maximum (\frac{73 - 1729}{6}, \frac{5183 + 1729 1729}{54}), Minimum (\frac{73 + 1729}{6}, \frac{5183 - 1729 1729}{54})

Graph

Beliebte Beispiele

extreme f(x)=x^3-y^3+3x^2+3y^2-9x+5

e x t re m e f (x) = x^{3} - y^{3} + 3 x^{2} + 3 y^{2} - 9 x + 5

extreme f(x)= 4/3 x^3-25/2 x^2+6x+4

e x t re m e f (x) = \frac{4}{3} x^{3} - \frac{25}{2} x^{2} + 6 x + 4

extreme f(xy)=x^2y-15xy^2+12y

e x t re m e f (x y) = x^{2} y - 15 x y^{2} + 12 y

extreme f(x)=12x^2-18x

e x t re m e f (x) = 12 x^{2} - 18 x

extreme-6x^5+180x^3-1350x+14

e x t re m e - 6 x^{5} + 180 x^{3} - 1350 x + 14