How to calculate minimum value of a function?

Question

$min $ $f(x)=(x_{1}-2)^2 + (x_{2}-1)^2 $

Hint a sum of squares is never negative. Then the question is, can it be zero? — Macavity, Sep 16 '14 at 19:24

score 5 · Accepted Answer · answered Sep 16 '14 at 19:25

5

I'm guessing that $\;x=(x_1,x_2)\;$ , and then

$$f(x)\ge 0\;\;\forall\;x\in\Bbb R^2\;,\;\;\;and\;\;\;\; f(2,1)=0$$

so...

answered Sep 16 '14 at 19:25

Timbuc

score 2 · Answer 2 · answered Sep 16 '14 at 19:28

2

HINT : Note that $$(x_1-2)^2\ge 0,\ \ \ (x_2-1)^2\ge 0$$ for $x_1,x_2\in\mathbb R$.

answered Sep 16 '14 at 19:28

mathlove

2 Answers2