extreme f(x)=x(16-41+2x)(41/2-x)

Lösung

extrempunkte

f (x) = x (16 - 41 + 2 x) (\frac{41}{2} - x)

Minimum (\frac{66 - 1281}{6}, - \frac{5643 + 427 1281}{18}), Maximum (\frac{66 + 1281}{6}, \frac{427 1281 - 5643}{18})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 132 x - \frac{1025}{2}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{427}{2 3} + 11,

Ansteigend

: - \frac{427}{2 3} + 11 < x < \frac{427}{2 3} + 11,

Absteigend

: \frac{427}{2 3} + 11 < x < \infty

Stecke

x = \frac{66 - 1281}{6}

x (16 - 41 + 2 x) (\frac{41}{2} - x) : - \frac{5643 + 427 1281}{18}

Minimum (\frac{66 - 1281}{6}, - \frac{5643 + 427 1281}{18})

Stecke

x = \frac{66 + 1281}{6}

x (16 - 41 + 2 x) (\frac{41}{2} - x) : \frac{427 1281 - 5643}{18}

Maximum (\frac{66 + 1281}{6}, \frac{427 1281 - 5643}{18})

Minimum (\frac{66 - 1281}{6}, - \frac{5643 + 427 1281}{18}), Maximum (\frac{66 + 1281}{6}, \frac{427 1281 - 5643}{18})