extreme f(x)=-x^3+2x^2+15x-5

Lösung

extrempunkte

f (x) = - x^{3} + 2 x^{2} + 15 x - 5

Minimum (- \frac{5}{3}, - \frac{535}{27}), Maximum (3, 31)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

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

Ansteigend

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

Absteigend

: 3 < x < \infty

Stecke

x = - \frac{5}{3}

- x^{3} + 2 x^{2} + 15 x - 5 : - \frac{535}{27}

Minimum (- \frac{5}{3}, - \frac{535}{27})

Stecke

x = 3

- x^{3} + 2 x^{2} + 15 x - 5 : 31

Maximum (3, 31)

Minimum (- \frac{5}{3}, - \frac{535}{27}), Maximum (3, 31)

d o main f (x) = \frac{56 x + 49}{x ^{2}}

in v erse f (x) = \frac{5}{5 x - 16}

in t erce pt s f (y) = 4 x + 12

r an g e \frac{x ^{3} - 3 x ^{2} - 4 x}{x - 4}

r an g e f (x) = x + 4 - x^{2}