extreme f(x)=150x+18x^2-1.5x^3

Lösung

extrempunkte

f (x) = 150 x + 18 x^{2} - 1.5 x^{3}

Minimum (- \frac{2 ( 111 - 6 )}{3}, - 247.51783 \dots), Maximum (\frac{2 ( 6 + 111 )}{3}, 1831.51783 \dots)

Schritte zur Lösung

f^{'} (x) = 150 + 36 x - 4.5 x^{2}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{2 37}{3} + 4,

Ansteigend

: - \frac{2 37}{3} + 4 < x < \frac{2 37}{3} + 4,

Absteigend

: \frac{2 37}{3} + 4 < x < \infty

Stecke

x = - \frac{2 ( 111 - 6 )}{3}

150 x + 18 x^{2} - 1.5 x^{3} : - 247.51783 \dots

Minimum (- \frac{2 ( 111 - 6 )}{3}, - 247.51783 \dots)

Stecke

x = \frac{2 ( 6 + 111 )}{3}

150 x + 18 x^{2} - 1.5 x^{3} : 1831.51783 \dots

Maximum (\frac{2 ( 6 + 111 )}{3}, 1831.51783 \dots)

Minimum (- \frac{2 ( 111 - 6 )}{3}, - 247.51783 \dots), Maximum (\frac{2 ( 6 + 111 )}{3}, 1831.51783 \dots)

e x t re m e f (x) = sin^{2} (2 x) - cos^{2} (2 x) - 1

e x t re m e f (x) = 2 x - 4 cos (x), - 2 \leq x \leq 0

e x t re m e f (x) = (x + 1) ln^{2} (x + 1)

e x t re m e f (x) = x^{2} - 6 x - 1, 0 \leq x \leq 3

e x t re m e f (x, y) = - x^{2} - y^{2} + x + 2 y - 1