extreme f(x)=x^3-3/2 x^2-6x+1

Lösung

extrempunkte

f (x) = x^{3} - \frac{3}{2} x^{2} - 6 x + 1

Maximum (- 1, \frac{9}{2}), Minimum (2, - 9)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 3 x - 6

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 1

x^{3} - \frac{3}{2} x^{2} - 6 x + 1 : \frac{9}{2}

Maximum (- 1, \frac{9}{2})

Stecke

x = 2

x^{3} - \frac{3}{2} x^{2} - 6 x + 1 : - 9

Minimum (2, - 9)

Maximum (- 1, \frac{9}{2}), Minimum (2, - 9)

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

e x t re m e f (x) = 600 + 35 x

e x t re m e f (x) = 3 cos (π x), 0 \leq x \leq \frac{1}{6}

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

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