extreme f(x)=-4x^3+3x^2+18x

Lösung

extrempunkte

f (x) = - 4 x^{3} + 3 x^{2} + 18 x

Minimum (- 1, - 11), Maximum (\frac{3}{2}, \frac{81}{4})

Schritte zur Lösung

f^{'} (x) = - 12 x^{2} + 6 x + 18

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < \frac{3}{2},

Absteigend

: \frac{3}{2} < x < \infty

Stecke

x = - 1

- 4 x^{3} + 3 x^{2} + 18 x : - 11

Minimum (- 1, - 11)

Stecke

x = \frac{3}{2}

- 4 x^{3} + 3 x^{2} + 18 x : \frac{81}{4}

Maximum (\frac{3}{2}, \frac{81}{4})

Minimum (- 1, - 11), Maximum (\frac{3}{2}, \frac{81}{4})

e x t re m e f (x, y) = 2 x^{2} - 8 x + y^{2} + 16 y + 100

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

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

e x t re m e f (x, y) = 9 - 2 x + 4 y - x^{2} - 4 y^{2}

e x t re m e f (x, y) = 36 - 9 x^{2} - 4 y^{2}