Differentation help

So for the ENGAA 2016 Section 2 Q2d, I don't really understand why it says "You may find it helpful to use the fact that any value of R_3 that maximises P also minimises 1/P"
Differentiating P (from part 2c) or 1/P and making them = 0 both give you the same answer that P is a minimum when R_3 = (R_1)/2, so why would that statement be helpful? Thanks in advance


Links to solutions and questions
https://www.physicsandmathstutor.com/admissions/engaa/solutions-2016/

https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FAdmissions%2FENGAA%2FPapers%2FENGAA%25202016%2520Section%25202.pdf

Looks like for P youd differentiate using the quotient rule then argue that numerator = 0. For 1/P you can do some algebraic simplification before the differentiation, as per the mark scheme, which is a bit simpler, but tbh there isnt much in it either way and as you say obviously you have to get the same answer.

A slightly different way to do the 1/P one is to note its simplified form is proportional to
(2sqrt(R3) + R1/sqrt(R3))^2
This is minimized when
2sqrt(R3) = R1 / sqrt(R3)
or R3 = R1/2. So it can be done calculus free but not sure its much easier.

Oh ok, thanks very much