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Beliebt Funktionen >

extreme 6x^4-8x^3-87x^2+90x+24

Lösung

extrempunkte

6 x^{4} - 8 x^{3} - 87 x^{2} + 90 x + 24

Lösung

Minimum (- \frac{5}{2}, - \frac{3083}{8}), Maximum (\frac{1}{2}, \frac{373}{8}), Minimum (3, - 219)

Schritte zur Lösung

f^{'} (x) = 24 x^{3} - 24 x^{2} - 174 x + 90

Intervalle finden:

Absteigend

: - \infty < x < - \frac{5}{2},

Ansteigend

: - \frac{5}{2} < x < \frac{1}{2},

Absteigend

: \frac{1}{2} < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - \frac{5}{2}

in

6 x^{4} - 8 x^{3} - 87 x^{2} + 90 x + 24 : - \frac{3083}{8}

Minimum (- \frac{5}{2}, - \frac{3083}{8})

Stecke

x = \frac{1}{2}

in

6 x^{4} - 8 x^{3} - 87 x^{2} + 90 x + 24 : \frac{373}{8}

Maximum (\frac{1}{2}, \frac{373}{8})

Stecke

x = 3

in

6 x^{4} - 8 x^{3} - 87 x^{2} + 90 x + 24 : - 219

Minimum (3, - 219)

Minimum (- \frac{5}{2}, - \frac{3083}{8}), Maximum (\frac{1}{2}, \frac{373}{8}), Minimum (3, - 219)

Graph

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