extreme f(x)=((500+500x))/(1+0.04x^2)

Lösung

extrempunkte

f (x) = \frac{( 500 + 500 \cdot x )}{1 + 0.04 \cdot x ^{2}}

Minimum (- 1 - 26, - 1024.75487 \dots), Maximum (26 - 1, 1524.75487 \dots)

Schritte zur Lösung

f^{'} (x) = \frac{- 20 x ^{2} - 40 x + 500}{( 1 + 0.04 x ^{2} ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 1 - 26,

Ansteigend

: - 1 - 26 < x < - 1 + 26,

Absteigend

: - 1 + 26 < x < \infty

Stecke

x = - 1 - 26

\frac{500 + 500 \cdot x}{1 + 0.04 \cdot x ^{2}} : - 1024.75487 \dots

Minimum (- 1 - 26, - 1024.75487 \dots)

Stecke

x = 26 - 1

\frac{500 + 500 \cdot x}{1 + 0.04 \cdot x ^{2}} : 1524.75487 \dots

Maximum (26 - 1, 1524.75487 \dots)

Minimum (- 1 - 26, - 1024.75487 \dots), Maximum (26 - 1, 1524.75487 \dots)

e x t re m e \frac{( x ^{2} + 2 )}{( x ^{2} - 16 )}

e x t re m e y = 2 x^{2} + 5

e x t re m e f (x) = 5 x^{4} - 20 x^{3} + 1

e x t re m e f (x) = 0.001 x^{2} + 3.2 x - 10

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