extreme f(x)=4x^3-36x^2+6

Lösung

extrempunkte

f (x) = 4 x^{3} - 36 x^{2} + 6

Maximum (0, 6), Minimum (6, - 426)

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 72 x

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = 0

4 x^{3} - 36 x^{2} + 6 : 6

Maximum (0, 6)

Stecke

x = 6

4 x^{3} - 36 x^{2} + 6 : - 426

Minimum (6, - 426)

Maximum (0, 6), Minimum (6, - 426)

e x t re m e f (x) = x^{2} + y^{2} - 14 x + 12 y - 13

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

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

e x t re m e f (x) = 25 x + \frac{16}{x}

e x t re m e f (x) = x^{2} - 2 x - 3, 0 \leq x \leq 1