# Problems related to Maxwell relations

## Homework Statement

Given the entropy of a system :
$$S = AU^αV^βN^{1-α-β}$$
The problem requires me to write
$$(\frac{∂T}{∂U})_{V,N} > 0, (\frac{∂P}{∂V})_{U,N} < 0, (\frac{∂μ}{∂N})_{U,V} > 0$$
to find the mathematical constraint of α and β

## Homework Equations

dU = TdS - PdV + μdN

## The Attempt at a Solution

Actually, I don't quite understand the rationale behind Maxwell relations.
I tried to write
dF = SdT - PdV + μdN
I can then get
$$(\frac {∂T} {∂F})_{V,N}$$
but I just don't know how to transform the variable. Can anyone give me an idea of these kind of problems. Thanks!