I have a quadratic function: $f(x) = 24x_1+14x_2+x_1x_2$ and point $x_0 = (2,10)^T$ with $f(x_0) = 208$
And the first question is "give descent direction r in $x_0$" The second question "is f convex in direction r?
How can I do that? I've already determine gradient and Hessean. But which step should be next? According to descent ditrection I fount such formula in the Inet: $r=-\partial{^2}f(x)\partial{f(x)}$ Is that formula correct?
About second question: If Hessean is positive for any x, it means, that f is convex But how to determine whether f convex $\mathbf{in}$ $\mathbf{direction }$?