extreme f(x)=2x^3+6x^2-48x+6[4.6]

Lösung

extrempunkte

f (x) = 2 x^{3} + 6 x^{2} - 48 x + 6 [4.6]

Maximum (- 4, 187.6), Minimum (2, - 28.4)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} + 12 x - 48

Intervalle finden:

Ansteigend

: - \infty < x < - 4,

Absteigend

: - 4 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 4

2 x^{3} + 6 x^{2} - 48 x + 6 [4.6] : 187.6

Maximum (- 4, 187.6)

Stecke

x = 2

2 x^{3} + 6 x^{2} - 48 x + 6 [4.6] : - 28.4

Minimum (2, - 28.4)

Maximum (- 4, 187.6), Minimum (2, - 28.4)

e x t re m e f (x) = 3 sin (x), - π \leq x \leq 2 π

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

e x t re m e f (x) = x^{3} - \frac{9}{2} x^{2} - 54 x + 12

e x t re m e y = x^{2} - 3 x - 70

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