How do I calculate vibrational zero point energy from a plot of heat capacity vs T

alberrace

I have a question in which I am to calculate vibrational zero point energy - I know the simplest way is to calculate the 'missing' area in the graph which is approximately equal to the zero point energy. How to I show that this area is related to the zero point energy?

I have numerous data points for temperature and specific heat capacity and told the substance is pure germanium. For a matter of interest is there a more mathematical derivation of zero point energy?

Thanks,

A