extreme 1/3 x^3-4x^2+12x+200

Lösung

extrempunkte

\frac{1}{3} x^{3} - 4 x^{2} + 12 x + 200

Maximum (2, \frac{632}{3}), Minimum (6, 200)

Schritte zur Lösung

f^{'} (x) = x^{2} - 8 x + 12

Intervalle finden:

Ansteigend

: - \infty < x < 2,

Absteigend

: 2 < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = 2

\frac{1}{3} x^{3} - 4 x^{2} + 12 x + 200 : \frac{632}{3}

Maximum (2, \frac{632}{3})

Stecke

x = 6

\frac{1}{3} x^{3} - 4 x^{2} + 12 x + 200 : 200

Minimum (6, 200)

Maximum (2, \frac{632}{3}), Minimum (6, 200)

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

e x t re m e f (x) = g (t) = 6 t^{4} - 8 t^{3} + 5

e x t re m e f (x) = - \frac{x ^{2}}{8} + \frac{y ^{2}}{78.13} + 8

e x t re m e f (x) = - (x - 4)^{2} \cdot (x + 4)^{2}

e x t re m e f (x, y) = x^{2} + y^{2} - 2 x + 10 y - 15