extreme f(x)=(900)/x+2pix^2

Lösung

extrempunkte

f (x) = \frac{900}{x} + 2 π x^{2}

Minimum (3 \frac{225}{π}, \frac{900 3 π}{3 225} + 2 π (\frac{225}{π})^{\frac{2}{3}})

Schritte zur Lösung

f^{'} (x) = - \frac{900}{x ^{2}} + 4 π x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 3 \frac{225}{π},

Ansteigend

: 3 \frac{225}{π} < x < \infty

Stecke

x = 3 \frac{225}{π}

\frac{900}{x} + 2 π x^{2} : \frac{900 3 π}{3 225} + 2 π (\frac{225}{π})^{\frac{2}{3}}

Minimum (3 \frac{225}{π}, \frac{900 3 π}{3 225} + 2 π (\frac{225}{π})^{\frac{2}{3}})

e x t re m e \frac{ln ( x )}{x ^{3}}

e x t re m e f (x) = - (25 - x^{2})^{2}

e x t re m e f (x) = (x - 3)^{\frac{4}{3}}

e x t re m e - \frac{5}{x - 6}

e x t re m e f (x) = \frac{3 x ^{5} - 20 x ^{3}}{32}