extreme f(x)= 1/2 x^4-2x^3-54x^2+15

Lösung

extrempunkte

f (x) = \frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15

Minimum (- 6, - 849), Maximum (0, 15), Minimum (9, - \frac{5073}{2})

Schritte zur Lösung

f^{'} (x) = 2 x^{3} - 6 x^{2} - 108 x

Intervalle finden:

Absteigend

: - \infty < x < - 6,

Ansteigend

: - 6 < x < 0,

Absteigend

: 0 < x < 9,

Ansteigend

: 9 < x < \infty

Stecke

x = - 6

\frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15 : - 849

Minimum (- 6, - 849)

Stecke

x = 0

\frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15 : 15

Maximum (0, 15)

Stecke

x = 9

\frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15 : - \frac{5073}{2}

Minimum (9, - \frac{5073}{2})

Minimum (- 6, - 849), Maximum (0, 15), Minimum (9, - \frac{5073}{2})

e x t re m e f (x) = ln (8 + 8 x^{3})

e x t re m e f (x) = sin (x) + x

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

e x t re m e f (x) = 3 x + 3 y

e x t re m e f (x) = \frac{- 7}{x ^{2} - 4}