extreme f(x)= 8/135 x^3-1/20 x^2-7/16 x

Lösung

extrempunkte

f (x) = \frac{8}{135} x^{3} - \frac{1}{20} x^{2} - \frac{7}{16} x

Maximum (- \frac{21}{16}, \frac{1813}{5120}), Minimum (\frac{15}{8}, - \frac{155}{256})

Schritte zur Lösung

f^{'} (x) = \frac{8 x ^{2}}{45} - \frac{x}{10} - \frac{7}{16}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{21}{16},

Absteigend

: - \frac{21}{16} < x < \frac{15}{8},

Ansteigend

: \frac{15}{8} < x < \infty

Stecke

x = - \frac{21}{16}

\frac{8}{135} x^{3} - \frac{1}{20} x^{2} - \frac{7}{16} x : \frac{1813}{5120}

Maximum (- \frac{21}{16}, \frac{1813}{5120})

Stecke

x = \frac{15}{8}

\frac{8}{135} x^{3} - \frac{1}{20} x^{2} - \frac{7}{16} x : - \frac{155}{256}

Minimum (\frac{15}{8}, - \frac{155}{256})

Maximum (- \frac{21}{16}, \frac{1813}{5120}), Minimum (\frac{15}{8}, - \frac{155}{256})

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

so l v e f or V, V = π r 2 h

e x t re m e f (x) = - 1000 x^{3} - 1000 x^{2} + 8000 x + 1000

e x t re m e \frac{1}{x} + ln (x)

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