1. The problem statement, all variables and given/known data This regards a question on heat capacity; I'm trying to find the temperature at which the heat capacity is maximum. After differentiating the heat capacity expression, equating to zero, and rearranging (all of which I have omitted), my problem boils down to: exp(x) = (x + 2)/(x - 2) Solve for x. (x in this context is theta/T, but I don't think it's relevant since I'm trying to find their ratio) 2. Relevant equations See above 3. The attempt at a solution I calculated x = 2.4 by trial-and-error, and the maximum heat hapacity for this value is in agreement with the my textbook. I just don't know how to solve it properly!