extreme f(x)=-(x^3)/3+2x^2+5x+1

Lösung

extrempunkte

f (x) = - \frac{x ^{3}}{3} + 2 x^{2} + 5 x + 1

Minimum (- 1, - \frac{5}{3}), Maximum (5, \frac{103}{3})

Schritte zur Lösung

f^{'} (x) = - x^{2} + 4 x + 5

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 5,

Absteigend

: 5 < x < \infty

Stecke

x = - 1

- \frac{x ^{3}}{3} + 2 x^{2} + 5 x + 1 : - \frac{5}{3}

Minimum (- 1, - \frac{5}{3})

Stecke

x = 5

- \frac{x ^{3}}{3} + 2 x^{2} + 5 x + 1 : \frac{103}{3}

Maximum (5, \frac{103}{3})

Minimum (- 1, - \frac{5}{3}), Maximum (5, \frac{103}{3})

e x t re m e \frac{7 x + 5}{x + 9} + \frac{8 x - 10}{x + 9}

e x t re m e x - 8 3 x

e x t re m e f (x) = x^{2} + x y + y^{2} - 22 y + 161

e x t re m e f (x) = x + \frac{4}{x}, 0.2 \leq x \leq 8

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