extreme f(x)= 1/3 x^3-9x^2+72x+2

Lösung

extrempunkte

f (x) = \frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2

Maximum (6, 182), Minimum (12, 146)

Schritte zur Lösung

f^{'} (x) = x^{2} - 18 x + 72

Intervalle finden:

Ansteigend

: - \infty < x < 6,

Absteigend

: 6 < x < 12,

Ansteigend

: 12 < x < \infty

Stecke

x = 6

\frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2 : 182

Maximum (6, 182)

Stecke

x = 12

\frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2 : 146

Minimum (12, 146)

Maximum (6, 182), Minimum (12, 146)

e x t re m e F (x, y) = x^{3} y^{2} + x^{2} y + 2 x y^{2} + 2 y

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

e x t re m e f (x) = (\frac{x}{5})^{5} - (\frac{4 x}{4})^{4} + 5

e x t re m e f (x) = x^{\frac{1}{3}} - x^{- \frac{2}{3}}

e x t re m e f (x) = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36