extreme f(x)=x^2log_{3}(x)

Lösung

extrempunkte

f (x) = x^{2} lo g_{3} (x)

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{3} (e))

Schritte zur Lösung

f^{'} (x) = \frac{x + 2 x ln ( x )}{ln ( 3 )}

Intervalle finden:

Absteigend

: 0 < x < \frac{1}{e},

Ansteigend

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

Stecke

x = \frac{1}{e}

x^{2} lo g_{3} (x) : - \frac{1}{2 e} lo g_{3} (e)

Minimum (\frac{1}{e}, - \frac{1}{2 e} lo g_{3} (e))

e x t re m e f (x) = \frac{x ^{2} - 9 x + 50}{x - 7}

e x t re m e - \frac{4}{x - 7}

e x t re m e f (x, y) = - 4 x^{2} - 2 y^{2} - 8 x + 12 y + 5

e x t re m e f (x, y) = \frac{4}{x + y}

e x t re m e f (x) = - x^{2} + 9, - 3 \leq x \leq 4