What is the extreme f(x,y)=100(y-x^2)^2+(1-x)^2 ?

The extreme f(x,y)=100(y-x^2)^2+(1-x)^2 is Minimum(1,1)

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extreme f(x,y)=100(y-x^2)^2+(1-x)^2

extreme

Minimum (1, 1)

Solution steps

Find the critical points:

(1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 200

D (x, y) = 80000 x^{2} - 80000 y + 400

Check the sign of at each critical point

Check critical point

(1, 1) :

Minimum

Minimum (1, 1)

What is the extreme f(x,y)=100(y-x^2)^2+(1-x)^2 ?
The extreme f(x,y)=100(y-x^2)^2+(1-x)^2 is Minimum(1,1)