extreme f(x)=x^3-4x^2-16x+9

Lösung

extrempunkte

f (x) = x^{3} - 4 x^{2} - 16 x + 9

Maximum (- \frac{4}{3}, \frac{563}{27}), Minimum (4, - 55)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 8 x - 16

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{4}{3},

Absteigend

: - \frac{4}{3} < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - \frac{4}{3}

x^{3} - 4 x^{2} - 16 x + 9 : \frac{563}{27}

Maximum (- \frac{4}{3}, \frac{563}{27})

Stecke

x = 4

x^{3} - 4 x^{2} - 16 x + 9 : - 55

Minimum (4, - 55)

Maximum (- \frac{4}{3}, \frac{563}{27}), Minimum (4, - 55)

cr i t i c a l f (x) = 2 x - 4 x

d o main f (x) = x + (1 - x)

m o n o t o n e y = \frac{x ^{2}}{( x - 2 ) ^{2}}

s l o p e - 2 x - 1

a sy m pt o t es f (x) = \frac{1 + e ^{- x}}{2 e ^{x}}