For example, suppose I have a function:
$$f(x_1,x_2,x_3) = x_1x_2 + x_1x_2 + x_1x_3$$
How can I show this is convex/concave or neither without using principal minors?
Is it just using the following?
$$f(y) - f(x) \leq Df(x)(y-x)$$
In that case, I would have some inequality to examine, but I'm unsure how to show if it is neither convex, nor concave (which is the answer I get using principal minors).