Hi guys For Q1 (ii) you need to differentiate the denomoinator of IR, set to zero and solve for alpha. I've tried using the chain rule for the differentiation. The result is something that isn't easy to solve. Is there an easier way of doing this or would you recommend just skipping such a question if it ever comes up again? My opinion right now is that it wouldn't be worth attempting a similar question.
Denominator of the IR is a squared-root. Indeed differentiating a squared-root function wouldn't be enjoying! However minimizing Standard Deviation (i.e. the denominator) is essentially minimizing Variance. So you can just "ignore" the "1/2" and differentiate what is inside. Then it shouldn't be too hard though simple chain rule will still be applicable to the contents. Hope it helps!
The alternative is to use the result in the notes (Chapter 17 page 26 of 2009 notes). The derivation of this is in Q17.15.
