extreme f(x)=(6x^2-x^4)/9

Lösung

extrempunkte

f (x) = \frac{6 x ^{2} - x ^{4}}{9}

Maximum (- 1.73205 \dots, 1), Minimum (0.00000 \dots, 0.00000 \dots), Maximum (1.73205 \dots, 1.00000 \dots)

Schritte zur Lösung

f^{'} (x) = \frac{1}{9} (12 x - 4 x^{3})

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 0,

Ansteigend

: 0 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 1.73205 \dots

\frac{6 x ^{2} - x ^{4}}{9} : 1

Maximum (- 1.73205 \dots, 1)

Stecke

x = 0.00000 \dots

\frac{6 x ^{2} - x ^{4}}{9} : 0.00000 \dots

Minimum (0.00000 \dots, 0.00000 \dots)

Stecke

x = 1.73205 \dots

\frac{6 x ^{2} - x ^{4}}{9} : 1.00000 \dots

Maximum (1.73205 \dots, 1.00000 \dots)

Maximum (- 1.73205 \dots, 1), Minimum (0.00000 \dots, 0.00000 \dots), Maximum (1.73205 \dots, 1.00000 \dots)

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

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

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

e x t re m e 25 - x^{2} - y^{2}

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