What is the extreme f(x,y)=(x-1)^2+(y-4)^2 ?

The extreme f(x,y)=(x-1)^2+(y-4)^2 is Minimum(1,4)

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extreme f(x,y)=(x-1)^2+(y-4)^2

extreme points

f (x, y) = (x - 1)^{2} + (y - 4)^{2}

Minimum (1, 4)

Solution steps

Find the critical points:

(1, 4)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(1, 4) :

Minimum

Minimum (1, 4)

5 x + \frac{100}{x}

f (x) = 3 x^{3} - 9 x^{2} - 315 x + 7

f (x) = \frac{2 x ^{2}}{x - 2}, (- 2, 1)

f (x) = 250 (0.9)^{x}, 0 \leq x \leq 6

y ln (x) + x y^{2}

What is the extreme f(x,y)=(x-1)^2+(y-4)^2 ?
The extreme f(x,y)=(x-1)^2+(y-4)^2 is Minimum(1,4)