extreme f(x)=-7/3 x^3+14x^2+147x+2

Lösung

extrempunkte

f (x) = - \frac{7}{3} x^{3} + 14 x^{2} + 147 x + 2

Minimum (- 3, - 250), Maximum (7, \frac{2750}{3})

Schritte zur Lösung

f^{'} (x) = - 7 x^{2} + 28 x + 147

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 7,

Absteigend

: 7 < x < \infty

Stecke

x = - 3

- \frac{7}{3} x^{3} + 14 x^{2} + 147 x + 2 : - 250

Minimum (- 3, - 250)

Stecke

x = 7

- \frac{7}{3} x^{3} + 14 x^{2} + 147 x + 2 : \frac{2750}{3}

Maximum (7, \frac{2750}{3})

Minimum (- 3, - 250), Maximum (7, \frac{2750}{3})

e x t re m e 3 t (8 - t)

e x t re m e f (x) = - x^{2} + 50 ln (x)

e x t re m e f (x) = - 69.7 x^{2} + 625.6 x

e x t re m e f (x) = \frac{1}{2} (x + 4)^{2} + 6

e x t re m e f (x, y) = x y + e^{x y}