What is the extreme f(x)=g(x,y)=(x-8)^2+(y-2)^2 ?

The extreme f(x)=g(x,y)=(x-8)^2+(y-2)^2 is Minimum(8,2)

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extreme f(x)=g(x,y)=(x-8)^2+(y-2)^2

extreme points

f (x) = g (x, y) = (x - 8)^{2} + (y - 2)^{2}

Minimum (8, 2)

Solution steps

Find the critical points:

(8, 2)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(8, 2) :

Minimum

Minimum (8, 2)

f (x) = 7 + 5 x + x^{2}

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

f (x, y) = x^{2} + 2 x y + x^{2}

f (x, y) = y + x y^{4}

f (x) = x^{4} + 32 x^{2}

What is the extreme f(x)=g(x,y)=(x-8)^2+(y-2)^2 ?
The extreme f(x)=g(x,y)=(x-8)^2+(y-2)^2 is Minimum(8,2)