extreme f(x)=4x^3-80x^2+300x

Lösung

extrempunkte

f (x) = 4 x^{3} - 80 x^{2} + 300 x

Maximum (\frac{5 ( 4 - 7 )}{3}, 500 (4 - 7) + \frac{20500 7 - 64000}{27}), Minimum (\frac{5 ( 4 + 7 )}{3}, 500 (4 + 7) + \frac{- 64000 - 20500 7}{27})

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 160 x + 300

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 5 7 + 20}{3},

Absteigend

: \frac{- 5 7 + 20}{3} < x < \frac{5 7 + 20}{3},

Ansteigend

: \frac{5 7 + 20}{3} < x < \infty

Stecke

x = \frac{5 ( 4 - 7 )}{3}

4 x^{3} - 80 x^{2} + 300 x : 500 (4 - 7) + \frac{20500 7 - 64000}{27}

Maximum (\frac{5 ( 4 - 7 )}{3}, 500 (4 - 7) + \frac{20500 7 - 64000}{27})

Stecke

x = \frac{5 ( 4 + 7 )}{3}

4 x^{3} - 80 x^{2} + 300 x : 500 (4 + 7) + \frac{- 64000 - 20500 7}{27}

Minimum (\frac{5 ( 4 + 7 )}{3}, 500 (4 + 7) + \frac{- 64000 - 20500 7}{27})

Maximum (\frac{5 ( 4 - 7 )}{3}, 500 (4 - 7) + \frac{20500 7 - 64000}{27}), Minimum (\frac{5 ( 4 + 7 )}{3}, 500 (4 + 7) + \frac{- 64000 - 20500 7}{27})

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

a sy m pt o t es ln (x + 4)

d o main \frac{x ^{2} + x - 2}{x ^{2} - 3 x - 4}

in v erse f (x) = 4 x^{2} + 8 x - 20

r an g e (x + 1)^{2} - 9