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

Lösung

extrempunkte

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

Maximum (- \frac{3}{5}, \frac{36}{25}), Minimum (\frac{1}{3}, - \frac{16}{27})

Schritte zur Lösung

f^{'} (x) = 15 x^{2} + 4 x - 3

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{3}{5},

Absteigend

: - \frac{3}{5} < x < \frac{1}{3},

Ansteigend

: \frac{1}{3} < x < \infty

Stecke

x = - \frac{3}{5}

5 x^{3} + 2 x^{2} - 3 x : \frac{36}{25}

Maximum (- \frac{3}{5}, \frac{36}{25})

Stecke

x = \frac{1}{3}

5 x^{3} + 2 x^{2} - 3 x : - \frac{16}{27}

Minimum (\frac{1}{3}, - \frac{16}{27})

Maximum (- \frac{3}{5}, \frac{36}{25}), Minimum (\frac{1}{3}, - \frac{16}{27})

e x t re m e f (x) = \frac{x}{x ^{2} + y ^{2}}

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

e x t re m e f (x, y) = 2 x^{3} - 3 x^{2} + 2 y^{3} - 6 y^{2}

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

e x t re m e f (x) = - 9 x^{2} + 126 x - 45