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Beliebt Funktionen >

extreme f(x)= 2/3 x^3-7/2 x^2+3x+16

Lösung

extrempunkte

f (x) = \frac{2}{3} x^{3} - \frac{7}{2} x^{2} + 3 x + 16

Lösung

Maximum (\frac{1}{2}, \frac{401}{24}), Minimum (3, \frac{23}{2})

Schritte zur Lösung

f^{'} (x) = 2 x^{2} - 7 x + 3

Intervalle finden:

Ansteigend

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

Absteigend

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

Ansteigend

: 3 < x < \infty

Stecke

x = \frac{1}{2}

in

\frac{2}{3} x^{3} - \frac{7}{2} x^{2} + 3 x + 16 : \frac{401}{24}

Maximum (\frac{1}{2}, \frac{401}{24})

Stecke

x = 3

in

\frac{2}{3} x^{3} - \frac{7}{2} x^{2} + 3 x + 16 : \frac{23}{2}

Minimum (3, \frac{23}{2})

Maximum (\frac{1}{2}, \frac{401}{24}), Minimum (3, \frac{23}{2})

Graph

Beliebte Beispiele

extreme sqrt(x)ln(3x)

e x t re m e x ln (3 x)

extreme f(x)= 1/x-ln(x)

e x t re m e f (x) = \frac{1}{x} - ln (x)

extreme f(x)=-2x^3+42x^2-240x+5

e x t re m e f (x) = - 2 x^{3} + 42 x^{2} - 240 x + 5

extreme y=6x-x^2-2

e x t re m e y = 6 x - x^{2} - 2

extreme f(x)= 1/((x^2-2x+7))

e x t re m e f (x) = \frac{1}{( x ^{2} - 2 x + 7 )}