extreme f(x)=2x^3+3x^2-36x+1[-6.3]

Lösung

extrempunkte

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 1 [- 6.3]

Maximum (- 3, 74.7), Minimum (2, - 50.3)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} + 6 x - 36

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 3

2 x^{3} + 3 x^{2} - 36 x + 1 [- 6.3] : 74.7

Maximum (- 3, 74.7)

Stecke

x = 2

2 x^{3} + 3 x^{2} - 36 x + 1 [- 6.3] : - 50.3

Minimum (2, - 50.3)

Maximum (- 3, 74.7), Minimum (2, - 50.3)

e x t re m e f (x) = e^{3 x} (3 - x)

e x t re m e f (x) = 4 x^{3} + 6 x^{2} - 24 x

e x t re m e f (x) = x^{2} - x - 3, 0 \leq x \leq 3

e x t re m e f (x) = - 4 x^{6} ln (3 x)

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