extreme f(x)= 3/4 x^4-3x^3-81x^2-16

Lösung

extrempunkte

f (x) = \frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16

Minimum (- 6, - 1312), Maximum (0, - 16), Minimum (9, - \frac{15373}{4})

Schritte zur Lösung

f^{'} (x) = 3 x^{3} - 9 x^{2} - 162 x

Intervalle finden:

Absteigend

: - \infty < x < - 6,

Ansteigend

: - 6 < x < 0,

Absteigend

: 0 < x < 9,

Ansteigend

: 9 < x < \infty

Stecke

x = - 6

\frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16 : - 1312

Minimum (- 6, - 1312)

Stecke

x = 0

\frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16 : - 16

Maximum (0, - 16)

Stecke

x = 9

\frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16 : - \frac{15373}{4}

Minimum (9, - \frac{15373}{4})

Minimum (- 6, - 1312), Maximum (0, - 16), Minimum (9, - \frac{15373}{4})

e x t re m e f (x) = - 5 (x - 4)^{4} + 2

e x t re m e f (x) = x^{2} - 5

e x t re m e f (x, y) = 5 e^{7 x y}

e x t re m e f (x) = 8 ln (x) - x^{2}

e x t re m e f (x) = 3 x^{4} + 4 x^{3} - 36 x^{2} - 78