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Beliebt Funktionen >

extreme f(x)= 2/3 x^3+11/2 x^2-21x+5

Lösung

extrempunkte

f (x) = \frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5

Lösung

Maximum (- 7, \frac{1157}{6}), Minimum (\frac{3}{2}, - \frac{95}{8})

Schritte zur Lösung

f^{'} (x) = 2 x^{2} + 11 x - 21

Intervalle finden:

Ansteigend

: - \infty < x < - 7,

Absteigend

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

Ansteigend

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

Stecke

x = - 7

in

\frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5 : \frac{1157}{6}

Maximum (- 7, \frac{1157}{6})

Stecke

x = \frac{3}{2}

in

\frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5 : - \frac{95}{8}

Minimum (\frac{3}{2}, - \frac{95}{8})

Maximum (- 7, \frac{1157}{6}), Minimum (\frac{3}{2}, - \frac{95}{8})

Graph

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