Convexity of a function in $\mathbb{R^2}$ I have to find if this function is convex or not...
$$f(x_1, x_2) = 2x_1^2 −x_1x_2 + x_2^2 −3x_1 + e^{2x_1+x_2}$$
For me its convex (I have plot the surface and it seems convex). To prove it, I tried many things but It didn't work.
First, $2x_1^2$, $x_2^2$ and $e^{2x_1+x_2}$ are convex (trivial), $-3x_1$ is affine so also convex. Now, I have to show that $−x_1x_2$ but I am not really sure of that
Thank you in advance !

Hint: $-x_1 x_2$ is not convex, but you can combine it with the other quadratic terms.
