What is the extreme f(x)=x-rx(1-x) ?

The extreme f(x)=x-rx(1-x) is Saddle(0,1),Saddle(1,-1)

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extreme f(x)=x-rx(1-x)

extreme points

f (x) = x - r x (1 - x)

Saddle (0, 1), Saddle (1, - 1)

Solution steps

Find the critical points:

(0, 1), (1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, r) = - 4 x^{2} + 4 x - 1

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Check critical point

(1, - 1) :

Saddle

Saddle (0, 1), Saddle (1, - 1)

f (x, y) = x^{3} + y^{3} + 3 x^{2} - 6 y^{2} - 5

f (x) = 0.01 x^{3} - 0.45 x^{2} + 2.43 x + 300

f (x) = (x - 2)^{3} + x^{2} - 1

f (x) = \frac{1}{2} x^{4} - 4 x^{3} + 8 x^{2} + 46

f (x) = - x^{4} + 8 x^{2} + 5

What is the extreme f(x)=x-rx(1-x) ?
The extreme f(x)=x-rx(1-x) is Saddle(0,1),Saddle(1,-1)