extreme 3+4x^2-x^4

Lösung

extrempunkte

3 + 4 x^{2} - x^{4}

Maximum (- 2, 7), Minimum (0, 3), Maximum (2, 7)

Schritte zur Lösung

f^{'} (x) = - 4 x^{3} + 8 x

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 2

3 + 4 x^{2} - x^{4} : 7

Maximum (- 2, 7)

Stecke

x = 0

3 + 4 x^{2} - x^{4} : 3

Minimum (0, 3)

Stecke

x = 2

3 + 4 x^{2} - x^{4} : 7

Maximum (2, 7)

Maximum (- 2, 7), Minimum (0, 3), Maximum (2, 7)

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

e x t re m e f (x, y) = \frac{x ^{4} + 2 x ^{3} y ^{2} + 2}{3 ( x - 1 ) y}

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

e x t re m e x^{2} - 5 x y + 4 y^{2} - 2 x + 5 y

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