If you are asked to derive the proportion xA which minimises the portfolio variance, is it necessary in the exam to perform second order differentiation to confirm your expression for xA does indeed minimise the portfolio variance?
It's always safest to check the second derivative. If you're pushed for time, or if you think that the number of marks available isn't worth the effort, then just say that it's something that should be checked, but that you're not going to. At least it shows the examiners that you're aware of the issue and that you've got a way to fix it.
