extreme f(x)=(-2)/3 x^3+9x^2-28x+1

Lösung

extrempunkte

f (x) = \frac{- 2}{3} x^{3} + 9 x^{2} - 28 x + 1

Minimum (2, - \frac{73}{3}), Maximum (7, \frac{52}{3})

Schritte zur Lösung

f^{'} (x) = - 2 x^{2} + 18 x - 28

Intervalle finden:

Absteigend

: - \infty < x < 2,

Ansteigend

: 2 < x < 7,

Absteigend

: 7 < x < \infty

Stecke

x = 2

\frac{- 2}{3} x^{3} + 9 x^{2} - 28 x + 1 : - \frac{73}{3}

Minimum (2, - \frac{73}{3})

Stecke

x = 7

\frac{- 2}{3} x^{3} + 9 x^{2} - 28 x + 1 : \frac{52}{3}

Maximum (7, \frac{52}{3})

Minimum (2, - \frac{73}{3}), Maximum (7, \frac{52}{3})

e x t re m e y = \frac{1}{x ^{2} - 1}

e x t re m e f (x, y) = (x^{2} - 25)^{2} + (y^{2} - 9)^{2}

e x t re m e f (x) = 4 cos (2 x) + 1, (0, 2 π)

e x t re m e 2 x y - 5 x^{2} - 2 y^{2} + 4 x + 4 y - 4

e x t re m e f (x) = x^{2} - 11, - 2 \leq x \leq 4