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Beliebt Funktionen >

extreme f(x)=4x^3+21x^2-294x+9

Lösung

extrempunkte

f (x) = 4 x^{3} + 21 x^{2} - 294 x + 9

Lösung

Maximum (- 7, 1724), Minimum (\frac{7}{2}, - \frac{2365}{4})

Schritte zur Lösung

f^{'} (x) = 12 x^{2} + 42 x - 294

Intervalle finden:

Ansteigend

: - \infty < x < - 7,

Absteigend

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

Ansteigend

: \frac{7}{2} < x < \infty

Stecke

x = - 7

in

4 x^{3} + 21 x^{2} - 294 x + 9 : 1724

Maximum (- 7, 1724)

Stecke

x = \frac{7}{2}

in

4 x^{3} + 21 x^{2} - 294 x + 9 : - \frac{2365}{4}

Minimum (\frac{7}{2}, - \frac{2365}{4})

Maximum (- 7, 1724), Minimum (\frac{7}{2}, - \frac{2365}{4})

Graph

Beliebte Beispiele

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

e x t re m e f (x) = (4 - x^{2})^{5}

extreme 2x+(27)/(x^2)

e x t re m e 2 x + \frac{27}{x ^{2}}

extreme f(x)=5x^2sqrt(1+x)

e x t re m e f (x) = 5 x^{2} 1 + x

extreme f(x)=x^3-3/2 x^2-18x

e x t re m e f (x) = x^{3} - \frac{3}{2} x^{2} - 18 x

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

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