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Beliebt Funktionen >

extreme f(x)=x^2sqrt(4-x^2)

Lösung

extrempunkte

f (x) = x^{2} 4 - x^{2}

Lösung

Minimum (- 2, 0), Maximum (- \frac{2 2}{3}, \frac{16}{3 3}), Minimum (0, 0), Maximum (\frac{2 2}{3}, \frac{16}{3 3}), Minimum (2, 0)

Schritte zur Lösung

f^{'} (x) = x (2 - (x + 2) (x - 2) - \frac{x ^{2}}{- ( x + 2 ) ( x - 2 )})

Intervalle finden:

Ansteigend

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

Absteigend

: - \frac{2 2}{3} < x < 0,

Ansteigend

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

Absteigend

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

Stecke

x = - 2

in

x^{2} 4 - x^{2} : 0

Minimum (- 2, 0)

Stecke

x = - \frac{2 2}{3}

in

x^{2} 4 - x^{2} : \frac{16}{3 3}

Maximum (- \frac{2 2}{3}, \frac{16}{3 3})

Stecke

x = 0

in

x^{2} 4 - x^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{2 2}{3}

in

x^{2} 4 - x^{2} : \frac{16}{3 3}

Maximum (\frac{2 2}{3}, \frac{16}{3 3})

Stecke

x = 2

in

x^{2} 4 - x^{2} : 0

Minimum (2, 0)

Minimum (- 2, 0), Maximum (- \frac{2 2}{3}, \frac{16}{3 3}), Minimum (0, 0), Maximum (\frac{2 2}{3}, \frac{16}{3 3}), Minimum (2, 0)

Graph

Beliebte Beispiele

invers f(x)=5-8x

in v erse f (x) = 5 - 8 x

domäne (16-t)^{1/8}

d o main (16 - t)^{\frac{1}{8}}

invers x^2-4x+3

in v erse x^{2} - 4 x + 3

invers f(x)=(x+2)/(x-6)

in v erse f (x) = \frac{x + 2}{x - 6}

critical f(x)=5x^2+4x

cr i t i c a l f (x) = 5 x^{2} + 4 x