extreme f(x)=x^3-15x^2+12x+7

Lösung

extrempunkte

f (x) = x^{3} - 15 x^{2} + 12 x + 7

Maximum (5 - 21, 4221 - 183), Minimum (5 + 21, - 183 - 4221)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 30 x + 12

Intervalle finden:

Ansteigend

: - \infty < x < - 21 + 5,

Absteigend

: - 21 + 5 < x < 21 + 5,

Ansteigend

: 21 + 5 < x < \infty

Stecke

x = 5 - 21

x^{3} - 15 x^{2} + 12 x + 7 : 4221 - 183

Maximum (5 - 21, 4221 - 183)

Stecke

x = 5 + 21

x^{3} - 15 x^{2} + 12 x + 7 : - 183 - 4221

Minimum (5 + 21, - 183 - 4221)

Maximum (5 - 21, 4221 - 183), Minimum (5 + 21, - 183 - 4221)

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

e x t re m e f (x, y) = x^{2} + y^{2} + 16

e x t re m e f (x, y) = 9 - 2 \cdot x + 4 \cdot y - x^{2} - 4 \cdot y^{2}

e x t re m e x ln (4 x)

e x t re m e f (x) = 2 x^{2} + 7 x