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

Lösung

extrempunkte

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

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

Schritte zur Lösung

f^{'} (x) = - \frac{x}{- x ^{2} + 4}

Intervalle finden:

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 2

Stecke

x = - 2

- x^{2} + 4 : 0

Minimum (- 2, 0)

Stecke

x = 0

- x^{2} + 4 : 2

Maximum (0, 2)

Stecke

x = 2

- x^{2} + 4 : 0

Minimum (2, 0)

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

e x t re m e f (x) = 2 x^{3} - 24 x, - 4 \leq x \leq 4

e x t re m e \frac{1}{4} x^{4} + \frac{1}{2} x^{3} - 3 x^{2} + 8

e x t re m e \frac{1}{4} x^{4} + \frac{1}{2} x^{3} - 3 x^{2} + 2

e x t re m e f (x) = x (25 - 39 + 2 x) (\frac{39}{2} - x)

e x t re m e f (x) = x^{2} + 8 x + 11