I have the following function : $f(x,y)=(1-x)^2+10(y-x^2)^2$
To prove that $f(x,y)$ is convex we need to calculate the Hessian matrix :
$\nabla^2f(x,y)=\pmatrix{120x^2-40y+2&-40x \\ -40x&20}$
This function is convex only if : $120x^2-40y+2> 0$ and $det(H)>0$
I'm stuck here and not able to prove $120x^2-40y+2> 0$ and $det(H)>0$.