extreme f(x)=(10x^3)/3-(11x^2)/2+x+2

Lösung

extrempunkte

f (x) = \frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2

Maximum (\frac{1}{10}, \frac{1229}{600}), Minimum (1, \frac{5}{6})

Schritte zur Lösung

f^{'} (x) = 10 x^{2} - 11 x + 1

Intervalle finden:

Ansteigend

: - \infty < x < \frac{1}{10},

Absteigend

: \frac{1}{10} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = \frac{1}{10}

\frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2 : \frac{1229}{600}

Maximum (\frac{1}{10}, \frac{1229}{600})

Stecke

x = 1

\frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2 : \frac{5}{6}

Minimum (1, \frac{5}{6})

Maximum (\frac{1}{10}, \frac{1229}{600}), Minimum (1, \frac{5}{6})

e x t re m e f (x) = x^{2} + 3, - 1 \leq x \leq 4

e x t re m e f (x, y) = 5 x + 5 y

e x t re m e f (x, y) = x^{2} - 2 y^{2} + 8 x - 3 y + 1

y = j + x

e x t re m e f (x, y) = 2 x^{2} + y^{2} - 2 x y + 5 x - 3 y + 1