Let $f:\mathbb R^n\to \mathbb R$, $f(x_1,x_2,...,x_n)=x_1^2+\dots +x_n^2$ with the constraint $x_1+\dots +x_n=1$. Show that $f$ has a minimum point at $(\frac{1}n,...,\frac{1}n)$
Using the method of lagrange multipliers I found that the only critical point is $(\frac{1}n,...,\frac{1}n)$ but how can I determine that this point is in fact a minima? I would really appreciate yoru help