Suppose we have a function $$ f(x) = \frac{(\sum_{i=1}^{n} x_i)^2}{\sum_{i=1}^{n} x_i^2} ,$$ where $x = (x_1, x_2, \ldots, x_n) $ is a vector of non-negative real numbers. We want to determine the convexity of this function. Specifically, we want to answer the question:
Is the function $ f(x) $ convex for $ x \geq 0 $?
I would appriciate any help.