extreme f(x)=9+4x^2-x^4

Lösung

extrempunkte

f (x) = 9 + 4 x^{2} - x^{4}

Maximum (- 2, 13), Minimum (0, 9), Maximum (2, 13)

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

9 + 4 x^{2} - x^{4} : 13

Maximum (- 2, 13)

Stecke

x = 0

9 + 4 x^{2} - x^{4} : 9

Minimum (0, 9)

Stecke

x = 2

9 + 4 x^{2} - x^{4} : 13

Maximum (2, 13)

Maximum (- 2, 13), Minimum (0, 9), Maximum (2, 13)

e x t re m e f (x) = x - ln (x), 0 \leq x \leq 2

e x t re m e y = \frac{1}{3} x^{3} + 2 x^{2} + 3 x

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

e x t re m e f (y) = 2 x^{2} - 9 x + 5

e x t re m e 2 x + 1 - 2 x