extreme 2(x-1)(x^2+1)(3x^2-2x+1)

Lösung

extrempunkte

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1)

Maximum (0.46612 \dots, - 0.93525 \dots), Minimum (0.65382 \dots, - 0.96342 \dots)

Schritte zur Lösung

Bestimme den kritischen Punkt:

x \approx 0.46612 \dots, x \approx 0.65382 \dots

Bereich von

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1) : - \infty < x < \infty

Intervalle finden:

Ansteigend

: - \infty < x < 0.46612 \dots,

Absteigend

: 0.46612 \dots < x < 0.65382 \dots,

Ansteigend

: 0.65382 \dots < x < \infty

Setz die Extremwerte

x = 0.46612 \dots

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1) \Rightarrow y = - 0.93525 \dots

ein

Maximum (0.46612 \dots, - 0.93525 \dots)

Setz die Extremwerte

x = 0.65382 \dots

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1) \Rightarrow y = - 0.96342 \dots

ein

Minimum (0.65382 \dots, - 0.96342 \dots)

Maximum (0.46612 \dots, - 0.93525 \dots), Minimum (0.65382 \dots, - 0.96342 \dots)

e x t re m e x^{3} + 30 x + 128

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

e x t re m e f (x, y) = x^{3} - 24 x + y^{3} - 10 y

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

e x t re m e y = x^{2} + \frac{250}{x}