extreme x^3-12x^2+45x+8

Lösung

extrempunkte

x^{3} - 12 x^{2} + 45 x + 8

Maximum (3, 62), Minimum (5, 58)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 24 x + 45

Intervalle finden:

Ansteigend

: - \infty < x < 3,

Absteigend

: 3 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = 3

x^{3} - 12 x^{2} + 45 x + 8 : 62

Maximum (3, 62)

Stecke

x = 5

x^{3} - 12 x^{2} + 45 x + 8 : 58

Minimum (5, 58)

Maximum (3, 62), Minimum (5, 58)

e x t re m e x^{4} - 4 x^{2} - 2, - 2 \leq x \leq 2

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

e x t re m e f (x) = \frac{8 x}{x ^{2} + 1}

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

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