extreme f(x)=-10/3 x^3-31/2 x^2-3x+4

Lösung

extrempunkte

f (x) = - \frac{10}{3} x^{3} - \frac{31}{2} x^{2} - 3 x + 4

Minimum (- 3, - \frac{73}{2}), Maximum (- \frac{1}{10}, \frac{2489}{600})

Schritte zur Lösung

f^{'} (x) = - 10 x^{2} - 31 x - 3

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < - \frac{1}{10},

Absteigend

: - \frac{1}{10} < x < \infty

Stecke

x = - 3

- \frac{10}{3} x^{3} - \frac{31}{2} x^{2} - 3 x + 4 : - \frac{73}{2}

Minimum (- 3, - \frac{73}{2})

Stecke

x = - \frac{1}{10}

- \frac{10}{3} x^{3} - \frac{31}{2} x^{2} - 3 x + 4 : \frac{2489}{600}

Maximum (- \frac{1}{10}, \frac{2489}{600})

Minimum (- 3, - \frac{73}{2}), Maximum (- \frac{1}{10}, \frac{2489}{600})

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