extreme y=(x^4)/(1+x^3)

Lösung

extrempunkte

y = \frac{x ^{4}}{1 + x ^{3}}

Maximum (- 34, - \frac{4 3 4}{3}), Minimum (0, 0)

Schritte zur Lösung

f^{'} (x) = \frac{4 x ^{3} + x ^{6}}{( 1 + x ^{3} ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 34,

Absteigend

: - 34 < x < - 1,

Absteigend

: - 1 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 34

\frac{x ^{4}}{1 + x ^{3}} : - \frac{4 3 4}{3}

Maximum (- 34, - \frac{4 3 4}{3})

Stecke

x = 0

\frac{x ^{4}}{1 + x ^{3}} : 0

Minimum (0, 0)

Maximum (- 34, - \frac{4 3 4}{3}), Minimum (0, 0)

e x t re m e \frac{200}{x + 4 + 2 x}

e x t re m e f (x) = - 0.3 t^{2} + 2.4 t + 98.2

e x t re m e f (x) = \frac{( x ^{2} - 8 )}{( x - 3 )}

e x t re m e f (x) = 4.3 x - 0.01 x^{2} - 8

e x t re m e f (x) = x^{5} - 3125 x, - 7 \leq x \leq 7