extreme 7x(1+12x^2)^{-2}

Lösung

extrempunkte

7 x (1 + 12 x^{2})^{- 2}

Minimum (- \frac{1}{6}, - \frac{21}{32}), Maximum (\frac{1}{6}, \frac{21}{32})

Schritte zur Lösung

f^{'} (x) = \frac{7 ( - 36 x ^{2} + 1 )}{( 12 x ^{2} + 1 ) ^{3}}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{6},

Ansteigend

: - \frac{1}{6} < x < \frac{1}{6},

Absteigend

: \frac{1}{6} < x < \infty

Stecke

x = - \frac{1}{6}

7 x (1 + 12 x^{2})^{- 2} : - \frac{21}{32}

Minimum (- \frac{1}{6}, - \frac{21}{32})

Stecke

x = \frac{1}{6}

7 x (1 + 12 x^{2})^{- 2} : \frac{21}{32}

Maximum (\frac{1}{6}, \frac{21}{32})

Minimum (- \frac{1}{6}, - \frac{21}{32}), Maximum (\frac{1}{6}, \frac{21}{32})

e x t re m e f (x) = 4 sin (x) + 3 cos (x), 0 \leq x \leq 2 π

e x t re m e f (x, y) = 2 x^{2} + 4 x y - x^{2} y - 4 x

e x t re m e f (x) = y e^{x} + x y^{2}

e x t re m e f (x) = x^{3} - 8 y^{3} + 4 x y - 8

e x t re m e 7 + 12 x - x^{3}