What is the extreme y=(5000)/(1+0.01e^{zx)} ?

The extreme y=(5000)/(1+0.01e^{zx)} is Saddle(0,0)

Popular >

extreme y=(5000)/(1+0.01e^{zx)}

extreme points

y = \frac{5000}{1 + 0.01 e ^{z x}}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial z ^{2}} = - \frac{50 e ^{z x} z ^{2} ( - 0.01 e ^{z x} + 1 )}{( 1 + 0.01 e ^{z x} ) ^{3}}

D (z, x) = \frac{- 5000 e ^{2 z x} z x + 0.5 e ^{4 z x} z x - 0.25 e ^{4 z x} - 50 e ^{3 z x} - 2500 e ^{2 z x}}{( 1 + 0.01 e ^{z x} ) ^{6}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 1 x - \frac{4}{3} x^{\frac{3}{4}}, (0, \infty)

f (x) = \frac{25 x}{x + 2} - x

y = x^{2} - 12

f (x) = 12 x^{2} - 180 x + 464

f (x) = - \frac{3}{16} x^{\frac{8}{3}} + \frac{3}{4} x^{\frac{2}{3}}

What is the extreme y=(5000)/(1+0.01e^{zx)} ?
The extreme y=(5000)/(1+0.01e^{zx)} is Saddle(0,0)