Question 1182171
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f(x,y) = x^2+y^2−4x−8y+30 fonksiyonunun minimum değerinin hangi x ve y noktalarında sağlandığını ve minimum değerin kaç olduğunu analitik çözümleyiniz<br>
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All those "funny" letters looked to me like Turkish, and I was right; here is how Google translator interpreted this:<br>
Analyze analytically at which x and y points the minimum value of the function is achieved and what the minimum value is.<br>
{{{f(x,y) = x^2+y^2-4x-8y+30}}}<br>
Complete the square in x and y:<br>
{{{f(x,y) = x^2-4x+y^2-8y+30}}}<br>
{{{f(x,y) = ((x^2-4x+4)+(y^2-8y+16)+30)-4-16}}}<br>
{{{f(x,y) = (x-2)^2+(y-4)^2+10}}}<br>
{{{(x-2)^2}}} and {{{(y-4)^2}}} both have minimum value 0 -- when x=2 and y=4.<br>
ANSWER: The minimum value, when x=2 and y=4, is 10.<br>