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Beliebt Funktionen >

extreme 2t^{10}(4-t^2)^5

Lösung

extrempunkte

2 t^{10} (4 - t^{2})^{5}

Lösung

Sattel (- 2, 0), Maximum (- 2, 2048), Minimum (0, 0), Maximum (2, 2048), Sattel (2, 0)

Schritte zur Lösung

f^{'} (t) = 2 (10 t^{9} (4 - t^{2})^{5} - 10 t^{11} (4 - t^{2})^{4})

Intervalle finden:

Ansteigend

: - \infty < t < - 2,

Ansteigend

: - 2 < t < - 2,

Absteigend

: - 2 < t < 0,

Ansteigend

: 0 < t < 2,

Absteigend

: 2 < t < 2,

Absteigend

: 2 < t < \infty

Stecke

t = - 2

in

2 t^{10} (4 - t^{2})^{5} : 0

Sattel (- 2, 0)

Stecke

t = - 2

in

2 t^{10} (4 - t^{2})^{5} : 2048

Maximum (- 2, 2048)

Stecke

t = 0

in

2 t^{10} (4 - t^{2})^{5} : 0

Minimum (0, 0)

Stecke

t = 2

in

2 t^{10} (4 - t^{2})^{5} : 2048

Maximum (2, 2048)

Stecke

t = 2

in

2 t^{10} (4 - t^{2})^{5} : 0

Sattel (2, 0)

Sattel (- 2, 0), Maximum (- 2, 2048), Minimum (0, 0), Maximum (2, 2048), Sattel (2, 0)

Graph

Beliebte Beispiele

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

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

extreme f(y)=x^3+y^3-27xy

e x t re m e f (y) = x^{3} + y^{3} - 27 x y

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

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

extreme f(x)=12x^2-88x+121

e x t re m e f (x) = 12 x^{2} - 88 x + 121

extreme f(x)=9x^3-7x^2+3x+10,-5<= x<= 6

e x t re m e f (x) = 9 x^{3} - 7 x^{2} + 3 x + 10, - 5 \leq x \leq 6