extreme x^3-12x^2+45x-4

Lösung

extrempunkte

x^{3} - 12 x^{2} + 45 x - 4

Maximum (3, 50), Minimum (5, 46)

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 - 4 : 50

Maximum (3, 50)

Stecke

x = 5

x^{3} - 12 x^{2} + 45 x - 4 : 46

Minimum (5, 46)

Maximum (3, 50), Minimum (5, 46)

e x t re m e f (x, y) = lo g_{10} (\frac{( x ^{2} + 2 \cdot y )}{( x + y ) ^{2}})

e x t re m e f (x) = y = tan (\frac{π x}{8}), 0 \leq x \leq 2

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

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

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