What is the minimum value of the function $y=sqrt(x²+2ax+10a²)$ where a > 0 ?

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Answer 1 · 2016-06-01T21:44:32

In order to find the minimum value of the function we have to minimize $g(x)=x^2+2ax+10a^2$ which occurs at

$g'(x)=0=>2x+2a=0=>x=-a$

and $g(-a)=9a^2$

Hence $f(-a)=sqrt(g(-a))=sqrt(9a^2)=3absa=3a$ since $a>0$

What is the minimum value of the function y=sqrt(x²+2ax+10a²)y=sqrt(x²+2ax+10a²) where a > 0 ?