What is the extreme f(x,y)=25*(y+x^2)^2+(1+x)^2 ?

The extreme f(x,y)=25*(y+x^2)^2+(1+x)^2 is Minimum(-1,-1)

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extreme f(x,y)=25*(y+x^2)^2+(1+x)^2

extreme points

f (x, y) = 25 \cdot (y + x^{2})^{2} + (1 + x)^{2}

Minimum (- 1, - 1)

Solution steps

Find the critical points:

(- 1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 50

D (x, y) = 5000 x^{2} + 5000 y + 100

Check the sign of at each critical point

Check critical point

(- 1, - 1) :

Minimum

Minimum (- 1, - 1)

f (x) = sin^{2} (x) - sin (x)

f (x) = 4 x^{3} + 9 x^{2} - 12 x + 7

h (v, t) = v t - 16 t^{2}

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

f (x) = x (x + a)

What is the extreme f(x,y)=25*(y+x^2)^2+(1+x)^2 ?
The extreme f(x,y)=25*(y+x^2)^2+(1+x)^2 is Minimum(-1,-1)