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Beliebt Funktionen >

extreme f(x)=(x^2-4)^4(x^2+1)^5

Lösung

extrempunkte

f (x) = (x^{2} - 4)^{4} (x^{2} + 1)^{5}

Lösung

Minimum (- 2, 0), Maximum (- \frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (0, 256), Maximum (\frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (2, 0)

Schritte zur Lösung

f^{'} (x) = 2 x (x + 2)^{3} (x - 2)^{3} (3 x + 4) (3 x - 4) (x^{2} + 1)^{4}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < - \frac{4}{3},

Absteigend

: - \frac{4}{3} < x < 0,

Ansteigend

: 0 < x < \frac{4}{3},

Absteigend

: \frac{4}{3} < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

in

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : 0

Minimum (- 2, 0)

Stecke

x = - \frac{4}{3}

in

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : \frac{5 ^{14} \cdot 256}{387420489}

Maximum (- \frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489})

Stecke

x = 0

in

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : 256

Minimum (0, 256)

Stecke

x = \frac{4}{3}

in

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : \frac{5 ^{14} \cdot 256}{387420489}

Maximum (\frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489})

Stecke

x = 2

in

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : 0

Minimum (2, 0)

Minimum (- 2, 0), Maximum (- \frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (0, 256), Maximum (\frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (2, 0)

Graph

Beliebte Beispiele

extreme f(x)=3x^4-54x^2+2

e x t re m e f (x) = 3 x^{4} - 54 x^{2} + 2

extreme f(x)=(log_{10}(x))/x

e x t re m e f (x) = \frac{lo g _{10} ( x )}{x}

extreme P(x,y)=3x+4y

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extreme f(1)=sqrt(x+3)

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extreme f(x)=4cos(3x)

e x t re m e f (x) = 4 cos (3 x)